What is expand ((x+h)^3)/h ?

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

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expand ((x+h)^3)/h

expand

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

\frac{x ^{3}}{h} + 3 x^{2} + 3 x h + h^{2}

Solution steps

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

(x + h)^{3} = x^{3} + 3 x^{2} h + 3 x h^{2} + h^{3}

= \frac{x ^{3} + 3 x ^{2} h + 3 x h ^{2} + h ^{3}}{h}

Apply the fraction rule:

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

\frac{x ^{3} + 3 x ^{2} h + 3 x h ^{2} + h ^{3}}{h} = \frac{x ^{3}}{h} + \frac{3 x ^{2} h}{h} + \frac{3 x h ^{2}}{h} + \frac{h ^{3}}{h}

= \frac{x ^{3}}{h} + \frac{3 x ^{2} h}{h} + \frac{3 x h ^{2}}{h} + \frac{h ^{3}}{h}

Cancel

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

= \frac{x ^{3}}{h} + 3 x^{2} + \frac{3 x h ^{2}}{h} + \frac{h ^{3}}{h}

Cancel

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

= \frac{x ^{3}}{h} + 3 x^{2} + 3 x h + \frac{h ^{3}}{h}

Cancel

\frac{h ^{3}}{h} : h^{2}

= \frac{x ^{3}}{h} + 3 x^{2} + 3 x h + h^{2}

(3 x^{2} y - 4 x y^{3} + 6 x) d x + (x^{3} - 6 x^{2} y^{2} - 1) d y

\frac{e ^{- 4 s} - e ^{- 6 s} + 2 s ^{2} + 8 s}{s ( s ^{2} + 4 s + 20 )}

\frac{\partial}{\partial x} ((z) (x y + x z^{3} - 2 yz))

\frac{( x - 3 ) ( x + 4 )}{( x + 3 ) ( - x ^{3} + 9 x ^{2} - 25 x + 35 )}

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