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$34$
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$\dfrac { 3 - \sqrt{ \color{#FF6800}{ 8 } } } { 3 + \sqrt{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\dfrac { 3 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 3 + \sqrt{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 3 + \sqrt{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 3 + \sqrt{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 - 2 \sqrt{ 2 } } { 3 + \sqrt{ \color{#FF6800}{ 8 } } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\dfrac { 3 - 2 \sqrt{ 2 } } { 3 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 - 2 \sqrt{ 2 } } { 3 + 2 \sqrt{ 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 - 2 \sqrt{ 2 } } { 3 + 2 \sqrt{ 2 } } \times \dfrac { 3 - \left ( 2 \sqrt{ 2 } \right ) } { 3 - \left ( 2 \sqrt{ 2 } \right ) } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { \left ( 3 + 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( 2 \sqrt{ 2 } \right ) \right ) } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { \left ( 3 + 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( 2 \sqrt{ 2 } \right ) \right ) } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } - \left ( 2 \sqrt{ 2 } \right ) ^ { 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Calculate power $ $
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \color{#FF6800}{ 9 } - \left ( 2 \sqrt{ 2 } \right ) ^ { 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Calculate power $ $
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - \color{#FF6800}{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Multiply $ 3 $ and $ 3$
$\dfrac { \color{#FF6800}{ 9 } + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 + 3 \times \left ( \color{#FF6800}{ - } \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Move the (-) sign forward $ $
$\dfrac { 9 \color{#FF6800}{ - } 3 \left ( 2 \sqrt{ 2 } \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 9 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Simplify the expression $ $
$\dfrac { 9 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 9 - 6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Simplify the expression $ $
$\dfrac { 9 - 6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Simplify the expression $ $
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 8 } } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Subtract $ 8 $ from $ 9$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 1 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 1 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\color{#FF6800}{ 9 } - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Add $ 9 $ and $ 8$
$\color{#FF6800}{ 17 } - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$17 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$ $ Calculate between similar terms $ $
$17 \color{#FF6800}{ - } \color{#FF6800}{ 12 } \sqrt{ \color{#FF6800}{ 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + \sqrt{ \color{#FF6800}{ 8 } } } { 3 - \sqrt{ 8 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 3 - \sqrt{ 8 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - \sqrt{ \color{#FF6800}{ 8 } } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) }$
$ $ Get rid of unnecessary parentheses $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - 2 \sqrt{ 2 } }$
$ $ Find the conjugate irrational number of denominator $ $
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - 2 \sqrt{ 2 } } \times \dfrac { 3 - \left ( - 2 \sqrt{ 2 } \right ) } { 3 - \left ( - 2 \sqrt{ 2 } \right ) }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ \dfrac { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } }$
$17 - 12 \sqrt{ 2 } + \dfrac { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { \left ( 3 - 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( - 2 \sqrt{ 2 } \right ) \right ) }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$17 - 12 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { \left ( 3 - 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( - 2 \sqrt{ 2 } \right ) \right ) }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } - \left ( 2 \sqrt{ 2 } \right ) ^ { 2 } }$
$ $ Calculate power $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { \color{#FF6800}{ 9 } - \left ( 2 \sqrt{ 2 } \right ) ^ { 2 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - \color{#FF6800}{ 8 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$ $ Multiply $ 3 $ and $ 3$
$17 - 12 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 9 } + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$ $ Simplify the expression $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$ $ Get rid of unnecessary parentheses $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$ $ Simplify the expression $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 }$
$ $ Get rid of unnecessary parentheses $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 }$
$ $ Simplify the expression $ $
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \color{#FF6800}{ 8 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } }$
$ $ Subtract $ 8 $ from $ 9$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 1 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 1 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ 9 } + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 8 }$
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ 9 } + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \color{#FF6800}{ 8 }$
$ $ Add $ 9 $ and $ 8$
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ 17 } + 6 \sqrt{ 2 } + 6 \sqrt{ 2 }$
$17 - 12 \sqrt{ 2 } + 17 + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Calculate between similar terms $ $
$17 - 12 \sqrt{ 2 } + 17 + \color{#FF6800}{ 12 } \sqrt{ \color{#FF6800}{ 2 } }$
$17 \color{#FF6800}{ - } \color{#FF6800}{ 12 } \sqrt{ \color{#FF6800}{ 2 } } + 17 \color{#FF6800}{ + } \color{#FF6800}{ 12 } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Eliminate opponent number $ $
$17 + 17$
$\color{#FF6800}{ 17 } \color{#FF6800}{ + } \color{#FF6800}{ 17 }$
$ $ Add $ 17 $ and $ 17$
$\color{#FF6800}{ 34 }$
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