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Calculate the value
$\dfrac{ 3 }{ \sqrt{ 10 } + \sqrt{ 7 } }$
$\sqrt{ 10 } - \sqrt{ 7 }$
Calculate the value
$\dfrac { 3 } { \sqrt{ 10 } + \sqrt{ 7 } }$
 Find the conjugate irrational number of denominator 
$\color{#FF6800}{ \dfrac { 3 } { \sqrt{ 10 } + \sqrt{ 7 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 10 } - \sqrt{ 7 } } { \sqrt{ 10 } - \sqrt{ 7 } } }$
$\dfrac { 3 } { \sqrt{ 10 } + \sqrt{ 7 } } \times \dfrac { \sqrt{ 10 } - \sqrt{ 7 } } { \sqrt{ 10 } - \sqrt{ 7 } }$
 The denominator is multiplied by denominator, and the numerator is multiplied by numerator 
$\color{#FF6800}{ \dfrac { 3 \left ( \sqrt{ 10 } - \sqrt{ 7 } \right ) } { \left ( \sqrt{ 10 } + \sqrt{ 7 } \right ) \left ( \sqrt{ 10 } - \sqrt{ 7 } \right ) } }$
$\dfrac { \color{#FF6800}{ 3 } \left ( \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 7 } } \right ) } { \left ( \sqrt{ 10 } + \sqrt{ 7 } \right ) \left ( \sqrt{ 10 } - \sqrt{ 7 } \right ) }$
 Multiply each term in parentheses by $3$
$\dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 7 } } \right ) } { \left ( \sqrt{ 10 } + \sqrt{ 7 } \right ) \left ( \sqrt{ 10 } - \sqrt{ 7 } \right ) }$
$\dfrac { 3 \sqrt{ 10 } + 3 \times \left ( - \sqrt{ 7 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 7 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 7 } } \right ) }$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 3 \sqrt{ 10 } + 3 \times \left ( - \sqrt{ 7 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 10 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { 3 \sqrt{ 10 } + 3 \times \left ( - \sqrt{ 7 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 10 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \sqrt{ 7 } \right ) ^ { 2 } }$
 Calculate power 
$\dfrac { 3 \sqrt{ 10 } + 3 \times \left ( - \sqrt{ 7 } \right ) } { \color{#FF6800}{ 10 } - \left ( \sqrt{ 7 } \right ) ^ { 2 } }$
$\dfrac { 3 \sqrt{ 10 } + 3 \times \left ( - \sqrt{ 7 } \right ) } { 10 - \left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
 Calculate power 
$\dfrac { 3 \sqrt{ 10 } + 3 \times \left ( - \sqrt{ 7 } \right ) } { 10 - \color{#FF6800}{ 7 } }$
$\dfrac { 3 \sqrt{ 10 } + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 7 } } \right ) } { 10 - 7 }$
 Simplify the expression 
$\dfrac { 3 \sqrt{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 7 } } } { 10 - 7 }$
$\dfrac { 3 \sqrt{ 10 } - 3 \sqrt{ 7 } } { \color{#FF6800}{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 7 } }$
 Subtract $7$ from $10$
$\dfrac { 3 \sqrt{ 10 } - 3 \sqrt{ 7 } } { \color{#FF6800}{ 3 } }$
$\color{#FF6800}{ \dfrac { 3 \sqrt{ 10 } - 3 \sqrt{ 7 } } { 3 } }$
 Reduce the fraction 
$\sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 7 } }$
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