What is expand ((x+h)^2+5(x+h)-7)/h ?

The solution to expand ((x+h)^2+5(x+h)-7)/h is (x^2)/h+2x+h+(5x)/h+5-7/h

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expand ((x+h)^2+5(x+h)-7)/h

expand

\frac{( x + h ) ^{2} + 5 ( x + h ) - 7}{h}

\frac{x ^{2}}{h} + 2 x + h + \frac{5 x}{h} + 5 - \frac{7}{h}

Solution steps

\frac{( x + h ) ^{2} + 5 ( x + h ) - 7}{h}

Expand

(x + h)^{2} + 5 (x + h) - 7 : x^{2} + 2 x h + h^{2} + 5 x + 5 h - 7

= \frac{x ^{2} + 2 x h + h ^{2} + 5 x + 5 h - 7}{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 x + 5 h - 7}{h} = \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} + \frac{5 x}{h} + \frac{5 h}{h} - \frac{7}{h}

= \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} + \frac{5 x}{h} + \frac{5 h}{h} - \frac{7}{h}

Cancel

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

= \frac{x ^{2}}{h} + 2 x + \frac{h ^{2}}{h} + \frac{5 x}{h} + \frac{5 h}{h} - \frac{7}{h}

Cancel

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

= \frac{x ^{2}}{h} + 2 x + h + \frac{5 x}{h} + \frac{5 h}{h} - \frac{7}{h}

Cancel

\frac{5 h}{h} : 5

= \frac{x ^{2}}{h} + 2 x + h + \frac{5 x}{h} + 5 - \frac{7}{h}

\frac{e ^{- s} - e ^{- 2 s} + s ^{2}}{s ^{2} ( s ^{2} - 2 s + 1 )}

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

\frac{( x - 1 ) ( x - 8 )}{3 x ^{5} - 5 x ^{3} - 7 x - 3}

(- 6, 5) y (- 3, - 3)

(250 (s + 7) (s + 14)) \cdot (s (s^{2} + 14 s + 50))

What is expand ((x+h)^2+5(x+h)-7)/h ?
The solution to expand ((x+h)^2+5(x+h)-7)/h is (x^2)/h+2x+h+(5x)/h+5-7/h