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Formula
Calculate the value
$\dfrac{ \sqrt{ 3 } }{ 2 \sqrt{ 3 } -3 }$
$2 + \sqrt{ 3 }$
Calculate the value
$\dfrac { \sqrt{ 3 } } { 2 \sqrt{ 3 } - 3 }$
 Find the conjugate irrational number of denominator 
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 \sqrt{ 3 } - 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 2 \sqrt{ 3 } + 3 } { 2 \sqrt{ 3 } + 3 } }$
$\dfrac { \sqrt{ 3 } } { 2 \sqrt{ 3 } - 3 } \times \dfrac { 2 \sqrt{ 3 } + 3 } { 2 \sqrt{ 3 } + 3 }$
 The denominator is multiplied by denominator, and the numerator is multiplied by numerator 
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } \left ( 2 \sqrt{ 3 } + 3 \right ) } { \left ( 2 \sqrt{ 3 } - 3 \right ) \left ( 2 \sqrt{ 3 } + 3 \right ) } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) } { \left ( 2 \sqrt{ 3 } - 3 \right ) \left ( 2 \sqrt{ 3 } + 3 \right ) }$
 Multiply each term in parentheses by $\sqrt{ 3 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } { \left ( 2 \sqrt{ 3 } - 3 \right ) \left ( 2 \sqrt{ 3 } + 3 \right ) }$
$\dfrac { \sqrt{ 3 } \left ( 2 \sqrt{ 3 } \right ) + \sqrt{ 3 } \times 3 } { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) }$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { \sqrt{ 3 } \left ( 2 \sqrt{ 3 } \right ) + \sqrt{ 3 } \times 3 } { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { \sqrt{ 3 } \left ( 2 \sqrt{ 3 } \right ) + \sqrt{ 3 } \times 3 } { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } - 3 ^ { 2 } }$
 Calculate power 
$\dfrac { \sqrt{ 3 } \left ( 2 \sqrt{ 3 } \right ) + \sqrt{ 3 } \times 3 } { \color{#FF6800}{ 12 } - 3 ^ { 2 } }$
$\dfrac { \sqrt{ 3 } \left ( 2 \sqrt{ 3 } \right ) + \sqrt{ 3 } \times 3 } { 12 - \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } }$
 Calculate power 
$\dfrac { \sqrt{ 3 } \left ( 2 \sqrt{ 3 } \right ) + \sqrt{ 3 } \times 3 } { 12 - \color{#FF6800}{ 9 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 3 } \times 3 } { 12 - 9 }$
 Get rid of unnecessary parentheses 
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \times 3 } { 12 - 9 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \times 3 } { 12 - 9 }$
 Simplify the expression 
$\dfrac { \color{#FF6800}{ 6 } + \sqrt{ 3 } \times 3 } { 12 - 9 }$
$\dfrac { 6 + \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } { 12 - 9 }$
 Simplify the expression 
$\dfrac { 6 + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } } { 12 - 9 }$
$\dfrac { 6 + 3 \sqrt{ 3 } } { \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 9 } }$
 Subtract $9$ from $12$
$\dfrac { 6 + 3 \sqrt{ 3 } } { \color{#FF6800}{ 3 } }$
$\color{#FF6800}{ \dfrac { 6 + 3 \sqrt{ 3 } } { 3 } }$
 Reduce the fraction 
$\color{#FF6800}{ 2 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } }$
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