What is (u/4+4/(u^2))/u ?

The solution to (u/4+4/(u^2))/u is (u^3+16)/(4u^3)

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simplify (u/4+4/(u^2))/u

simplify

\frac{\frac{u}{4} + \frac{4}{u ^{2}}}{u}

\frac{u ^{3} + 16}{4 u ^{3}}

Solution steps

\frac{\frac{u}{4} + \frac{4}{u ^{2}}}{u}

Join

\frac{u}{4} + \frac{4}{u ^{2}} : \frac{u ^{3} + 16}{4 u ^{2}}

= \frac{\frac{u ^{3} + 16}{4 u ^{2}}}{u}

Apply the fraction rule:

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

= \frac{u ^{3} + 16}{4 u ^{2} u}

Simplify

u^{2} u : u^{3}

= \frac{u ^{3} + 16}{4 u ^{3}}

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