What is expand ((x+h)^2)/h ?

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

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expand ((x+h)^2)/h

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

\frac{8 x + 4 + x ^{2}}{3 x ^{3} ( 2 x + 1 )}

\frac{4 x ^{2} + 20 x + 11}{( x - 3 ) ( x + 4 ) ( x + 5 )}

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

40 (\frac{3 x - 15}{1})

4 (x - 1 - 2 (2 + x) = 0)