What is expand ((x^2+1)^3)/(6x) ?

The solution to expand ((x^2+1)^3)/(6x) is (x^5)/6+(x^3)/2+x/2+1/(6x)

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expand ((x^2+1)^3)/(6x)

expand

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

\frac{x ^{5}}{6} + \frac{x ^{3}}{2} + \frac{x}{2} + \frac{1}{6 x}

Solution steps

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

(x^{2} + 1)^{3} = x^{6} + 3 x^{4} + 3 x^{2} + 1

= \frac{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}{6 x}

Apply the fraction rule:

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

\frac{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}{6 x} = \frac{x ^{6}}{6 x} + \frac{3 x ^{4}}{6 x} + \frac{3 x ^{2}}{6 x} + \frac{1}{6 x}

= \frac{x ^{6}}{6 x} + \frac{3 x ^{4}}{6 x} + \frac{3 x ^{2}}{6 x} + \frac{1}{6 x}

Cancel

\frac{x ^{6}}{6 x} : \frac{x ^{5}}{6}

= \frac{x ^{5}}{6} + \frac{3 x ^{4}}{6 x} + \frac{3 x ^{2}}{6 x} + \frac{1}{6 x}

Cancel

\frac{3 x ^{4}}{6 x} : \frac{x ^{3}}{2}

= \frac{x ^{5}}{6} + \frac{x ^{3}}{2} + \frac{3 x ^{2}}{6 x} + \frac{1}{6 x}

Cancel

\frac{3 x ^{2}}{6 x} : \frac{x}{2}

= \frac{x ^{5}}{6} + \frac{x ^{3}}{2} + \frac{x}{2} + \frac{1}{6 x}

2 (b - e) + (f + c)^{2}

\frac{3}{2 ( 4 f - 10 )}

\frac{2 ( 1 + 7 )}{3}

\frac{3 s}{( s ^{2} + 1 ) ( s ^{2} + 4 )}

\frac{13 x - 6}{x ^{2} ( 2 x - 3 )}

What is expand ((x^2+1)^3)/(6x) ?
The solution to expand ((x^2+1)^3)/(6x) is (x^5)/6+(x^3)/2+x/2+1/(6x)