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Calculate the value
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$\sqrt{ 3 } \left( \dfrac{ 1 }{ \sqrt{ 3 } } + \dfrac{ 1 }{ \sqrt{ 5 } } \right) + \sqrt{ 5 } \left( \dfrac{ 1 }{ \sqrt{ 3 } } - \dfrac{ 1 }{ \sqrt{ 5 } } \right)$
$\dfrac { 8 \sqrt{ 15 } } { 15 }$
Calculate the value
$\sqrt{ 3 } \left ( \color{#FF6800}{ \dfrac { 1 } { \sqrt{ 3 } } } + \dfrac { 1 } { \sqrt{ 5 } } \right ) + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Calculate the expression $ $
$\sqrt{ 3 } \left ( \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 3 } } + \dfrac { 1 } { \sqrt{ 5 } } \right ) + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\sqrt{ 3 } \left ( \dfrac { \sqrt{ 3 } } { 3 } + \color{#FF6800}{ \dfrac { 1 } { \sqrt{ 5 } } } \right ) + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Calculate the expression $ $
$\sqrt{ 3 } \left ( \dfrac { \sqrt{ 3 } } { 3 } + \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 5 } } \right ) + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\sqrt{ 3 } \left ( \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 3 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 5 } } \right ) + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Find the sum of the fractions $ $
$\sqrt{ 3 } \times \color{#FF6800}{ \dfrac { 5 \sqrt{ 3 } + 3 \sqrt{ 5 } } { 15 } } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 5 \sqrt{ 3 } + 3 \sqrt{ 5 } } { 15 } } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Arrange the terms multiplied by fractions $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } \left ( 5 \sqrt{ 3 } + 3 \sqrt{ 5 } \right ) } { 15 } } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Multiply each term in parentheses by $ \sqrt{ 3 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 3 } \left ( 3 \sqrt{ 5 } \right ) } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \left ( 3 \sqrt{ 5 } \right ) } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \left ( 3 \sqrt{ 5 } \right ) } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Simplify the expression $ $
$\dfrac { \color{#FF6800}{ 15 } + \sqrt{ 3 } \left ( 3 \sqrt{ 5 } \right ) } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\dfrac { 15 + \sqrt{ \color{#FF6800}{ 3 } } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 15 + \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\dfrac { 15 + \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Simplify the expression $ $
$\dfrac { 15 + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 15 } } } { 15 } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\color{#FF6800}{ \dfrac { 15 + 3 \sqrt{ 15 } } { 15 } } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ \dfrac { 5 + \sqrt{ 15 } } { 5 } } + \sqrt{ 5 } \left ( \dfrac { 1 } { \sqrt{ 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \sqrt{ 5 } \left ( \color{#FF6800}{ \dfrac { 1 } { \sqrt{ 3 } } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$ $ Calculate the expression $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \sqrt{ 5 } \left ( \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 3 } } - \dfrac { 1 } { \sqrt{ 5 } } \right )$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \sqrt{ 5 } \left ( \dfrac { \sqrt{ 3 } } { 3 } - \color{#FF6800}{ \dfrac { 1 } { \sqrt{ 5 } } } \right )$
$ $ Calculate the expression $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \sqrt{ 5 } \left ( \dfrac { \sqrt{ 3 } } { 3 } - \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 5 } } \right )$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \sqrt{ 5 } \left ( \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 5 } } \right )$
$ $ Find the sum of the fractions $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \sqrt{ 5 } \times \color{#FF6800}{ \dfrac { 5 \sqrt{ 3 } - 3 \sqrt{ 5 } } { 15 } }$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 5 \sqrt{ 3 } - 3 \sqrt{ 5 } } { 15 } }$
$ $ Arrange the terms multiplied by fractions $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \color{#FF6800}{ \dfrac { \sqrt{ 5 } \left ( 5 \sqrt{ 3 } - 3 \sqrt{ 5 } \right ) } { 15 } }$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { 15 }$
$ $ Multiply each term in parentheses by $ \sqrt{ 5 }$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { 15 }$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 5 } \times \left ( - 3 \sqrt{ 5 } \right ) } { 15 }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 5 } \times \left ( - 3 \sqrt{ 5 } \right ) } { 15 }$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 5 } \times \left ( - 3 \sqrt{ 5 } \right ) } { 15 }$
$ $ Simplify the expression $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 15 } } + \sqrt{ 5 } \times \left ( - 3 \sqrt{ 5 } \right ) } { 15 }$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { 5 \sqrt{ 15 } + \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { 15 }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { 5 \sqrt{ 15 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } } { 15 }$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { 5 \sqrt{ 15 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } } { 15 }$
$ $ Simplify the expression $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \dfrac { 5 \sqrt{ 15 } \color{#FF6800}{ - } \color{#FF6800}{ 15 } } { 15 }$
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \color{#FF6800}{ \dfrac { 5 \sqrt{ 15 } - 15 } { 15 } }$
$ $ Reduce the fraction $ $
$\dfrac { 5 + \sqrt{ 15 } } { 5 } + \color{#FF6800}{ \dfrac { \sqrt{ 15 } - 3 } { 3 } }$
$\color{#FF6800}{ \dfrac { 5 + \sqrt{ 15 } } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \sqrt{ 15 } - 3 } { 3 } }$
$ $ Find the sum of the fractions $ $
$\color{#FF6800}{ \dfrac { 15 + 3 \sqrt{ 15 } + 5 \sqrt{ 15 } - 15 } { 15 } }$
$\dfrac { \color{#FF6800}{ 15 } + 3 \sqrt{ 15 } + 5 \sqrt{ 15 } \color{#FF6800}{ - } \color{#FF6800}{ 15 } } { 15 }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$\dfrac { 3 \sqrt{ 15 } + 5 \sqrt{ 15 } } { 15 }$
$\dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 15 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 15 } } } { 15 }$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 15 } } } { 15 }$
Solution search results
search-thumbnail-If the sum of two consecutive 
numbers is $45$ and one number is $X$ 
.This statement in the form of 
equation $1s:$ 
$\left(1$ Point) $\right)$ 
$○5x+1$ $1eft\left(x+1$ $r1gnt\right)=45s$ 
$○sx+1ef\left(x+2$ $r1gnt\right)=145s$ 
$sx+1x=45s$
7th-9th grade
Algebra
search-thumbnail-$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ 
$s1S$ 
$S-1S$ 
$s2S$ 
$s50s$
7th-9th grade
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