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Formula
Calculate the value
$6-3 \sqrt{ 5 } + \dfrac{ 1 }{ 6-3 \sqrt{ 5 } }$
$\dfrac { 16 - 10 \sqrt{ 5 } } { 3 }$
Calculate the value
$6 - 3 \sqrt{ 5 } + \dfrac { 1 } { 6 - 3 \sqrt{ 5 } }$
 Find the conjugate irrational number of denominator 
$6 - 3 \sqrt{ 5 } + \color{#FF6800}{ \dfrac { 1 } { 6 - 3 \sqrt{ 5 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { 6 - \left ( - 3 \sqrt{ 5 } \right ) } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 1 } { 6 - 3 \sqrt{ 5 } } \times \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { 6 - \left ( - 3 \sqrt{ 5 } \right ) }$
 The denominator is multiplied by denominator, and the numerator is multiplied by numerator 
$6 - 3 \sqrt{ 5 } + \color{#FF6800}{ \dfrac { 1 \left ( 6 - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \left ( 6 - 3 \sqrt{ 5 } \right ) \left ( 6 - \left ( - 3 \sqrt{ 5 } \right ) \right ) } }$
$6 - 3 \sqrt{ 5 } + \dfrac { \color{#FF6800}{ 1 } \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \right ) } { \left ( 6 - 3 \sqrt{ 5 } \right ) \left ( 6 - \left ( - 3 \sqrt{ 5 } \right ) \right ) }$
 Multiply each term in parentheses by $1$
$6 - 3 \sqrt{ 5 } + \dfrac { \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \right ) } { \left ( 6 - 3 \sqrt{ 5 } \right ) \left ( 6 - \left ( - 3 \sqrt{ 5 } \right ) \right ) }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \right ) }$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \color{#FF6800}{ 6 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \color{#FF6800}{ 6 } ^ { \color{#FF6800}{ 2 } } - \left ( 3 \sqrt{ 5 } \right ) ^ { 2 } }$
 Calculate power 
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \color{#FF6800}{ 36 } - \left ( 3 \sqrt{ 5 } \right ) ^ { 2 } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { 36 - \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
 Calculate power 
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { 36 - \color{#FF6800}{ 45 } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + \color{#FF6800}{ 1 } \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { 36 - 45 }$
 Multiplying any number by 1 does not change the value 
$6 - 3 \sqrt{ 5 } + \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { 36 - 45 }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { \color{#FF6800}{ 36 } \color{#FF6800}{ - } \color{#FF6800}{ 45 } }$
 Subtract $45$ from $36$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { \color{#FF6800}{ - } \color{#FF6800}{ 9 } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 3 \sqrt{ 5 } \right ) } { - 9 }$
 Simplify Minus 
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 3 \sqrt{ 5 } } { - 9 }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 3 \sqrt{ 5 } } { \color{#FF6800}{ - } \color{#FF6800}{ 9 } }$
 Move the minus sign to the front of the fraction 
$6 - 3 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 6 + 3 \sqrt{ 5 } } { 9 } }$
$6 - 3 \sqrt{ 5 } - \color{#FF6800}{ \dfrac { 6 + 3 \sqrt{ 5 } } { 9 } }$
 Reduce the fraction 
$6 - 3 \sqrt{ 5 } - \color{#FF6800}{ \dfrac { 2 + \sqrt{ 5 } } { 3 } }$
$\color{#FF6800}{ 6 } - 3 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 + \sqrt{ 5 } } { 3 } }$
 Find the sum of the fractions 
$\color{#FF6800}{ \dfrac { 18 - \left ( 2 + \sqrt{ 5 } \right ) } { 3 } } - 3 \sqrt{ 5 }$
$\dfrac { 18 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { 3 } - 3 \sqrt{ 5 }$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$\dfrac { 18 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } } { 3 } - 3 \sqrt{ 5 }$
$\dfrac { \color{#FF6800}{ 18 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } - \sqrt{ 5 } } { 3 } - 3 \sqrt{ 5 }$
 Subtract $2$ from $18$
$\dfrac { \color{#FF6800}{ 16 } - \sqrt{ 5 } } { 3 } - 3 \sqrt{ 5 }$
$\color{#FF6800}{ \dfrac { 16 - \sqrt{ 5 } } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } }$
 Find the sum of the fractions 
$\color{#FF6800}{ \dfrac { 16 - \sqrt{ 5 } - 9 \sqrt{ 5 } } { 3 } }$
$\dfrac { 16 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 9 } \sqrt{ \color{#FF6800}{ 5 } } } { 3 }$
 Calculate between similar terms 
$\dfrac { 16 \color{#FF6800}{ - } \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 5 } } } { 3 }$
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