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$\dfrac { 3 \sqrt{ 15 } - 2 \sqrt{ 6 } } { 3 }$
Calculate the value
$\color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } } { \sqrt{ \color{#FF6800}{ 3 } } } } + \dfrac { 2 } { 3 } \left ( \sqrt{ 15 } - \dfrac { \sqrt{ 6 } } { 2 } \right )$
$ $ Calculate the expression $ $
$\color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 3 } } } + \dfrac { 2 } { 3 } \left ( \sqrt{ 15 } - \dfrac { \sqrt{ 6 } } { 2 } \right )$
$\dfrac { \sqrt{ 15 } - \sqrt{ 6 } } { 3 } + \dfrac { 2 } { 3 } \left ( \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 2 } } } \right )$
$ $ Find the sum of the fractions $ $
$\dfrac { \sqrt{ 15 } - \sqrt{ 6 } } { 3 } + \dfrac { 2 } { 3 } \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 2 } } }$
$\dfrac { \sqrt{ 15 } - \sqrt{ 6 } } { 3 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 2 } } }$
$ $ Arrange the terms multiplied by fractions $ $
$\dfrac { \sqrt{ 15 } - \sqrt{ 6 } } { 3 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right ) } { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$\dfrac { \sqrt{ 15 } - \sqrt{ 6 } } { 3 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right ) } { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$ $ Reduce the fraction $ $
$\dfrac { \sqrt{ 15 } - \sqrt{ 6 } } { 3 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 3 } } }$
$\color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 3 } } }$
$ $ Combine the fraction with the same denominator $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { 3 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 15 } } - \sqrt{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } - \sqrt{ 6 } } { 3 }$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 15 } } - \sqrt{ 6 } - \sqrt{ 6 } } { 3 }$
$\dfrac { 3 \sqrt{ 15 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { 3 }$
$ $ Calculate between similar terms $ $
$\dfrac { 3 \sqrt{ 15 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } } { 3 }$
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