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$- 15 + 11 \sqrt{ 3 }$
Calculate the value
$\dfrac { 2 - \sqrt{ 3 } } { 7 - 4 \sqrt{ 3 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 2 - \sqrt{ 3 } } { 7 - 4 \sqrt{ 3 } } \times \dfrac { 7 - \left ( - 4 \sqrt{ 3 } \right ) } { 7 - \left ( - 4 \sqrt{ 3 } \right ) } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { \left ( 7 - 4 \sqrt{ 3 } \right ) \left ( 7 - \left ( - 4 \sqrt{ 3 } \right ) \right ) } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } } { \left ( 7 - 4 \sqrt{ 3 } \right ) \left ( 7 - \left ( - 4 \sqrt{ 3 } \right ) \right ) } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 2 \times 7 + 2 \times 4 \sqrt{ 3 } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 2 \times 7 + 2 \times 4 \sqrt{ 3 } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 2 \times 7 + 2 \times 4 \sqrt{ 3 } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } - \left ( 4 \sqrt{ 3 } \right ) ^ { 2 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Calculate power $ $
$\dfrac { 2 \times 7 + 2 \times 4 \sqrt{ 3 } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { \color{#FF6800}{ 49 } - \left ( 4 \sqrt{ 3 } \right ) ^ { 2 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 2 \times 7 + 2 \times 4 \sqrt{ 3 } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { 49 - \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Calculate power $ $
$\dfrac { 2 \times 7 + 2 \times 4 \sqrt{ 3 } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { 49 - \color{#FF6800}{ 48 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } + 2 \times 4 \sqrt{ 3 } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { 49 - 48 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Multiply $ 2 $ and $ 7$
$\dfrac { \color{#FF6800}{ 14 } + 2 \times 4 \sqrt{ 3 } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { 49 - 48 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 14 + \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { 49 - 48 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Simplify the expression $ $
$\dfrac { 14 + \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 3 } } - \sqrt{ 3 } \times 7 - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { 49 - 48 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 14 + 8 \sqrt{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { 49 - 48 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Simplify the expression $ $
$\dfrac { 14 + 8 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 3 } } - \sqrt{ 3 } \times 4 \sqrt{ 3 } } { 49 - 48 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 14 + 8 \sqrt{ 3 } - 7 \sqrt{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } } { 49 - 48 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Simplify the expression $ $
$\dfrac { 14 + 8 \sqrt{ 3 } - 7 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 12 } } { 49 - 48 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 14 + 8 \sqrt{ 3 } - 7 \sqrt{ 3 } - 12 } { \color{#FF6800}{ 49 } \color{#FF6800}{ - } \color{#FF6800}{ 48 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Subtract $ 48 $ from $ 49$
$\dfrac { 14 + 8 \sqrt{ 3 } - 7 \sqrt{ 3 } - 12 } { \color{#FF6800}{ 1 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\dfrac { 14 + 8 \sqrt{ 3 } - 7 \sqrt{ 3 } - 12 } { \color{#FF6800}{ 1 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\color{#FF6800}{ 14 } + \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 12 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$\color{#FF6800}{ 14 } + 8 \sqrt{ 3 } - 7 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 12 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Subtract $ 12 $ from $ 14$
$\color{#FF6800}{ 2 } + 8 \sqrt{ 3 } - 7 \sqrt{ 3 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$2 + \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 3 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Calculate between similar terms $ $
$2 + \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 3 } } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$2 + \color{#FF6800}{ 1 } \sqrt{ 3 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$2 + \sqrt{ 3 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$2 + \sqrt{ 3 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } }$
$ $ Find the conjugate irrational number of denominator $ $
$2 + \sqrt{ 3 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) } }$
$2 + \sqrt{ 3 } + \dfrac { 1 + 2 \sqrt{ 3 } } { 7 + 4 \sqrt{ 3 } } \times \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) } { 7 - \left ( 4 \sqrt{ 3 } \right ) }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$2 + \sqrt{ 3 } + \color{#FF6800}{ \dfrac { \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } }$
$2 + \sqrt{ 3 } + \dfrac { \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { \left ( 7 + 4 \sqrt{ 3 } \right ) \left ( 7 - \left ( 4 \sqrt{ 3 } \right ) \right ) }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$2 + \sqrt{ 3 } + \dfrac { \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { \left ( 7 + 4 \sqrt{ 3 } \right ) \left ( 7 - \left ( 4 \sqrt{ 3 } \right ) \right ) }$
$2 + \sqrt{ 3 } + \dfrac { 1 \times 7 + 1 \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$2 + \sqrt{ 3 } + \dfrac { 1 \times 7 + 1 \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$2 + \sqrt{ 3 } + \dfrac { 1 \times 7 + 1 \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } - \left ( 4 \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Calculate power $ $
$2 + \sqrt{ 3 } + \dfrac { 1 \times 7 + 1 \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { \color{#FF6800}{ 49 } - \left ( 4 \sqrt{ 3 } \right ) ^ { 2 } }$
$2 + \sqrt{ 3 } + \dfrac { 1 \times 7 + 1 \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$2 + \sqrt{ 3 } + \dfrac { 1 \times 7 + 1 \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - \color{#FF6800}{ 48 } }$
$2 + \sqrt{ 3 } + \dfrac { \color{#FF6800}{ 1 } \times 7 + 1 \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - 48 }$
$ $ Multiplying any number by 1 does not change the value $ $
$2 + \sqrt{ 3 } + \dfrac { \color{#FF6800}{ 7 } + 1 \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - 48 }$
$2 + \sqrt{ 3 } + \dfrac { 7 + \color{#FF6800}{ 1 } \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - 48 }$
$ $ Multiplying any number by 1 does not change the value $ $
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + \left ( 2 \sqrt{ 3 } \right ) \times 7 + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - 48 }$
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 7 } + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - 48 }$
$ $ Get rid of unnecessary parentheses $ $
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - 48 }$
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - 48 }$
$ $ Simplify the expression $ $
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + \color{#FF6800}{ 14 } \sqrt{ \color{#FF6800}{ 3 } } + \left ( 2 \sqrt{ 3 } \right ) \times \left ( - \left ( 4 \sqrt{ 3 } \right ) \right ) } { 49 - 48 }$
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + 14 \sqrt{ 3 } + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { 49 - 48 }$
$ $ Get rid of unnecessary parentheses $ $
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + 14 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } } { 49 - 48 }$
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + 14 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } } { 49 - 48 }$
$ $ Simplify the expression $ $
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + 14 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 24 } } { 49 - 48 }$
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + 14 \sqrt{ 3 } - 24 } { \color{#FF6800}{ 49 } \color{#FF6800}{ - } \color{#FF6800}{ 48 } }$
$ $ Subtract $ 48 $ from $ 49$
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + 14 \sqrt{ 3 } - 24 } { \color{#FF6800}{ 1 } }$
$2 + \sqrt{ 3 } + \dfrac { 7 - \left ( 4 \sqrt{ 3 } \right ) + 14 \sqrt{ 3 } - 24 } { \color{#FF6800}{ 1 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$2 + \sqrt{ 3 } + \color{#FF6800}{ 7 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \color{#FF6800}{ 14 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$2 + \sqrt{ 3 } + 7 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + 14 \sqrt{ 3 } - 24$
$ $ Get rid of unnecessary parentheses $ $
$2 + \sqrt{ 3 } + 7 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } + 14 \sqrt{ 3 } - 24$
$2 + \sqrt{ 3 } + \color{#FF6800}{ 7 } - 4 \sqrt{ 3 } + 14 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$ $ Subtract $ 24 $ from $ 7$
$2 + \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 17 } - 4 \sqrt{ 3 } + 14 \sqrt{ 3 }$
$2 + \sqrt{ 3 } - 17 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } + \color{#FF6800}{ 14 } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ Calculate between similar terms $ $
$2 + \sqrt{ 3 } - 17 + \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 3 } }$
$\color{#FF6800}{ 2 } + \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 17 } + 10 \sqrt{ 3 }$
$ $ Subtract $ 17 $ from $ 2$
$\color{#FF6800}{ - } \color{#FF6800}{ 15 } + \sqrt{ 3 } + 10 \sqrt{ 3 }$
$- 15 + \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ Calculate between similar terms $ $
$- 15 + \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } }$
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