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Calculate the value
$\dfrac{ \sqrt{ 3 } - \sqrt{ 2 } }{ \sqrt{ 3 } + \sqrt{ 2 } }$
$5 - 2 \sqrt{ 6 }$
Calculate the value
$\dfrac { \sqrt{ 3 } - \sqrt{ 2 } } { \sqrt{ 3 } + \sqrt{ 2 } }$
 Find the conjugate irrational number of denominator 
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } - \sqrt{ 2 } } { \sqrt{ 3 } + \sqrt{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 3 } - \sqrt{ 2 } } { \sqrt{ 3 } - \sqrt{ 2 } } }$
$\dfrac { \sqrt{ 3 } - \sqrt{ 2 } } { \sqrt{ 3 } + \sqrt{ 2 } } \times \dfrac { \sqrt{ 3 } - \sqrt{ 2 } } { \sqrt{ 3 } - \sqrt{ 2 } }$
 The denominator is multiplied by denominator, and the numerator is multiplied by numerator 
$\color{#FF6800}{ \dfrac { \left ( \sqrt{ 3 } - \sqrt{ 2 } \right ) \left ( \sqrt{ 3 } - \sqrt{ 2 } \right ) } { \left ( \sqrt{ 3 } + \sqrt{ 2 } \right ) \left ( \sqrt{ 3 } - \sqrt{ 2 } \right ) } }$
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { \left ( \sqrt{ 3 } + \sqrt{ 2 } \right ) \left ( \sqrt{ 3 } - \sqrt{ 2 } \right ) }$
 Expand using $\left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { \left ( \sqrt{ 3 } + \sqrt{ 2 } \right ) \left ( \sqrt{ 3 } - \sqrt{ 2 } \right ) }$
$\dfrac { \sqrt{ 3 } \sqrt{ 3 } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) }$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { \sqrt{ 3 } \sqrt{ 3 } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { \left ( \sqrt{ 3 } \right ) ^ { 2 } - \left ( \sqrt{ 2 } \right ) ^ { 2 } }$
 Arrange the expression 
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { \left ( \sqrt{ 3 } \right ) ^ { 2 } - \left ( \sqrt{ 2 } \right ) ^ { 2 } }$
$\dfrac { \sqrt{ 3 \times 3 } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \sqrt{ 2 } \right ) ^ { 2 } }$
 Calculate power 
$\dfrac { \sqrt{ 3 \times 3 } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { \color{#FF6800}{ 3 } - \left ( \sqrt{ 2 } \right ) ^ { 2 } }$
$\dfrac { \sqrt{ 3 \times 3 } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
 Calculate power 
$\dfrac { \sqrt{ 3 \times 3 } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - \color{#FF6800}{ 2 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - 2 }$
 Multiply $3$ and $3$
$\dfrac { \sqrt{ \color{#FF6800}{ 9 } } + \sqrt{ 3 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } + \sqrt{ 3 } \times \left ( \color{#FF6800}{ - } \sqrt{ 2 } \right ) - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - 2 }$
 Move the (-) sign forward 
$\dfrac { \sqrt{ 9 } \color{#FF6800}{ - } \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - 2 }$
 Calculate multiplication 
$\dfrac { \sqrt{ 9 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } - \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - 2 }$
 Calculate multiplication 
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } - \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 2 } \right ) } { 3 - 2 }$
 Since negative numbers are multiplied by an even number, remove the (-) sign 
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \sqrt{ 2 } \sqrt{ 2 } } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ 2 } } { 3 - 2 }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 2 } } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 2 } } } { 3 - 2 }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 3 - 2 }$
 Add the exponent as the base is the same 
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 3 - 2 }$
 Add $1$ and $1$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } } { 3 - 2 }$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { 2 } } { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } }$
 Subtract $2$ from $3$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { 2 } } { \color{#FF6800}{ 1 } }$
$\dfrac { \sqrt{ 9 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { 2 } } { \color{#FF6800}{ 1 } }$
 If the denominator is 1, the denominator can be removed 
$\sqrt{ \color{#FF6800}{ 9 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$\sqrt{ \color{#FF6800}{ 9 } } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { 2 }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$\color{#FF6800}{ 3 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 2 } \right ) ^ { 2 }$
$3 - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
 If you square the radical sign, it will disappear 
$3 - \sqrt{ 6 } - \sqrt{ 6 } + \color{#FF6800}{ 2 }$
$\color{#FF6800}{ 3 } - \sqrt{ 6 } - \sqrt{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
 Add $3$ and $2$
$\color{#FF6800}{ 5 } - \sqrt{ 6 } - \sqrt{ 6 }$
$5 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } }$
 Calculate between similar terms 
$5 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } }$
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