What is expand (15C+6(x-1)^{5/2}+10(x-1)^{3/2})/(15) ?

The solution to expand (15C+6(x-1)^{5/2}+10(x-1)^{3/2})/(15) is C+(2(x-1)^{5/2})/5+(2(x-1)^{3/2})/3

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expand (15C+6(x-1)^{5/2}+10(x-1)^{3/2})/(15)

expand

\frac{15 C + 6 ( x - 1 ) ^{\frac{5}{2}} + 10 ( x - 1 ) ^{\frac{3}{2}}}{15}

C + \frac{2 ( x - 1 ) ^{\frac{5}{2}}}{5} + \frac{2 ( x - 1 ) ^{\frac{3}{2}}}{3}

Solution steps

\frac{15 C + 6 ( x - 1 ) ^{\frac{5}{2}} + 10 ( x - 1 ) ^{\frac{3}{2}}}{15}

Apply the fraction rule:

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

\frac{15 C + 6 ( x - 1 ) ^{\frac{5}{2}} + 10 ( x - 1 ) ^{\frac{3}{2}}}{15} = \frac{15 C}{15} + \frac{6 ( x - 1 ) ^{\frac{5}{2}}}{15} + \frac{10 ( x - 1 ) ^{\frac{3}{2}}}{15}

= \frac{15 C}{15} + \frac{6 ( x - 1 ) ^{\frac{5}{2}}}{15} + \frac{10 ( x - 1 ) ^{\frac{3}{2}}}{15}

Divide the numbers:

\frac{15}{15} = 1

= C + \frac{6 ( x - 1 ) ^{\frac{5}{2}}}{15} + \frac{10 ( x - 1 ) ^{\frac{3}{2}}}{15}

Cancel

\frac{6 ( x - 1 ) ^{\frac{5}{2}}}{15} : \frac{2 ( x - 1 ) ^{\frac{5}{2}}}{5}

= C + \frac{2 ( x - 1 ) ^{\frac{5}{2}}}{5} + \frac{10 ( x - 1 ) ^{\frac{3}{2}}}{15}

Cancel

\frac{10 ( x - 1 ) ^{\frac{3}{2}}}{15} : \frac{2 ( x - 1 ) ^{\frac{3}{2}}}{3}

= C + \frac{2 ( x - 1 ) ^{\frac{5}{2}}}{5} + \frac{2 ( x - 1 ) ^{\frac{3}{2}}}{3}

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What is expand (15C+6(x-1)^{5/2}+10(x-1)^{3/2})/(15) ?
The solution to expand (15C+6(x-1)^{5/2}+10(x-1)^{3/2})/(15) is C+(2(x-1)^{5/2})/5+(2(x-1)^{3/2})/3