What is (1/((x+h)^3)-1/(x^3))/h ?

The solution to (1/((x+h)^3)-1/(x^3))/h is -(3x^2+3xh+h^2)/(x^3(x+h)^3)

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simplify (1/((x+h)^3)-1/(x^3))/h

simplify

\frac{\frac{1}{( x + h ) ^{3}} - \frac{1}{x ^{3}}}{h}

- \frac{3 x ^{2} + 3 x h + h ^{2}}{x ^{3} ( x + h ) ^{3}}

Solution steps

\frac{\frac{1}{( x + h ) ^{3}} - \frac{1}{x ^{3}}}{h}

Join

\frac{1}{( x + h ) ^{3}} - \frac{1}{x ^{3}} : \frac{- 3 x ^{2} h - 3 x h ^{2} - h ^{3}}{x ^{3} ( x + h ) ^{3}}

= \frac{\frac{- 3 x ^{2} h - 3 x h ^{2} - h ^{3}}{x ^{3} ( x + h ) ^{3}}}{h}

Apply the fraction rule:

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

= \frac{- 3 x ^{2} h - 3 x h ^{2} - h ^{3}}{x ^{3} ( x + h ) ^{3} h}

Cancel

\frac{- 3 x ^{2} h - 3 x h ^{2} - h ^{3}}{x ^{3} ( x + h ) ^{3} h} : - \frac{3 x ^{2} + 3 x h + h ^{2}}{x ^{3} ( x + h ) ^{3}}

= - \frac{3 x ^{2} + 3 x h + h ^{2}}{x ^{3} ( x + h ) ^{3}}

3 \leq 3 x - 4 \leq 2 x + 1

x^{2} - \frac{1}{4} x + \frac{1}{64}

\frac{\frac{7}{4}}{( - \frac{3}{2} )}

\frac{6 i}{1 - i}

n - 19 = - 22

What is (1/((x+h)^3)-1/(x^3))/h ?
The solution to (1/((x+h)^3)-1/(x^3))/h is -(3x^2+3xh+h^2)/(x^3(x+h)^3)