What is expand ((x+h)^2-5)/h ?

The solution to expand ((x+h)^2-5)/h is (x^2)/h+2x+h-5/h

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expand ((x+h)^2-5)/h

expand

\frac{( x + h ) ^{2} - 5}{h}

\frac{x ^{2}}{h} + 2 x + h - \frac{5}{h}

Solution steps

\frac{( x + h ) ^{2} - 5}{h}

Expand

(x + h)^{2} - 5 : x^{2} + 2 x h + h^{2} - 5

= \frac{x ^{2} + 2 x h + h ^{2} - 5}{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} - 5}{h} = \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} - \frac{5}{h}

= \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} - \frac{5}{h}

Cancel

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

= \frac{x ^{2}}{h} + 2 x + \frac{h ^{2}}{h} - \frac{5}{h}

Cancel

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

= \frac{x ^{2}}{h} + 2 x + h - \frac{5}{h}

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\frac{d}{d t} ((a) (300 + t)^{2})

What is expand ((x+h)^2-5)/h ?
The solution to expand ((x+h)^2-5)/h is (x^2)/h+2x+h-5/h