What is expand (2(50*5^{1/2}-18*3^{1/2}))/(15) ?

The solution to expand (2(50*5^{1/2}-18*3^{1/2}))/(15) is (20*5^{1/2})/3-(12*3^{1/2})/5

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expand (2(505^{1/2}-183^{1/2}))/(15)

expand

\frac{2 ( 50 \cdot 5 ^{\frac{1}{2}} - 18 \cdot 3 ^{\frac{1}{2}} )}{15}

\frac{20 \cdot 5 ^{\frac{1}{2}}}{3} - \frac{12 \cdot 3 ^{\frac{1}{2}}}{5}

Decimal Notation

10.75019 \dots

Solution steps

\frac{2 ( 50 \cdot 5 ^{\frac{1}{2}} - 18 \cdot 3 ^{\frac{1}{2}} )}{15}

Expand

2 (50 \cdot 5^{\frac{1}{2}} - 18 \cdot 3^{\frac{1}{2}}) : 100 \cdot 5^{\frac{1}{2}} - 36 \cdot 3^{\frac{1}{2}}

= \frac{100 \cdot 5 ^{\frac{1}{2}} - 36 \cdot 3 ^{\frac{1}{2}}}{15}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{100 \cdot 5 ^{\frac{1}{2}} - 36 \cdot 3 ^{\frac{1}{2}}}{15} = \frac{100 \cdot 5 ^{\frac{1}{2}}}{15} - \frac{36 \cdot 3 ^{\frac{1}{2}}}{15}

= \frac{100 \cdot 5 ^{\frac{1}{2}}}{15} - \frac{36 \cdot 3 ^{\frac{1}{2}}}{15}

Cancel

\frac{100 \cdot 5 ^{\frac{1}{2}}}{15} : \frac{20 \cdot 5 ^{\frac{1}{2}}}{3}

= \frac{20 \cdot 5 ^{\frac{1}{2}}}{3} - \frac{36 \cdot 3 ^{\frac{1}{2}}}{15}

Cancel

\frac{36 \cdot 3 ^{\frac{1}{2}}}{15} : \frac{12 \cdot 3 ^{\frac{1}{2}}}{5}

= \frac{20 \cdot 5 ^{\frac{1}{2}}}{3} - \frac{12 \cdot 3 ^{\frac{1}{2}}}{5}

\frac{10 - 7 x}{( x + 2 ) ( x - 2 )}

\frac{- x ^{6} + 3 x ^{2}}{( x ^{4} + 1 ) ^{2}}

(\frac{3 n}{3 n + 1}) - (\frac{3 n - 3}{3 n - 2})

6 (6 d + 8 e) + 2 (2 d - 9 e)

- \frac{7 s + 2 s ^{3}}{( s ^{2} + 4 ) ^{2}}

What is expand (2(50*5^{1/2}-18*3^{1/2}))/(15) ?
The solution to expand (2(50*5^{1/2}-18*3^{1/2}))/(15) is (20*5^{1/2})/3-(12*3^{1/2})/5