What is expand (-3(x+h)^2+3(x+h)-4)/h ?

The solution to expand (-3(x+h)^2+3(x+h)-4)/h is -(3x^2)/h-6x-3h+(3x)/h+3-4/h

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expand (-3(x+h)^2+3(x+h)-4)/h

expand

\frac{- 3 ( x + h ) ^{2} + 3 ( x + h ) - 4}{h}

- \frac{3 x ^{2}}{h} - 6 x - 3 h + \frac{3 x}{h} + 3 - \frac{4}{h}

Solution steps

\frac{- 3 ( x + h ) ^{2} + 3 ( x + h ) - 4}{h}

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

= \frac{- 3 ( x ^{2} + 2 x h + h ^{2} ) + 3 ( x + h ) - 4}{h}

Expand

- 3 (x^{2} + 2 x h + h^{2}) + 3 (x + h) - 4 : - 3 x^{2} - 6 x h - 3 h^{2} + 3 x + 3 h - 4

= \frac{- 3 x ^{2} - 6 x h - 3 h ^{2} + 3 x + 3 h - 4}{h}

Apply the fraction rule:

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

\frac{- 3 x ^{2} - 6 x h - 3 h ^{2} + 3 x + 3 h - 4}{h} = - \frac{3 x ^{2}}{h} - \frac{6 x h}{h} - \frac{3 h ^{2}}{h} + \frac{3 x}{h} + \frac{3 h}{h} - \frac{4}{h}

= - \frac{3 x ^{2}}{h} - \frac{6 x h}{h} - \frac{3 h ^{2}}{h} + \frac{3 x}{h} + \frac{3 h}{h} - \frac{4}{h}

Cancel

\frac{6 x h}{h} : 6 x

= - \frac{3 x ^{2}}{h} - 6 x - \frac{3 h ^{2}}{h} + \frac{3 x}{h} + \frac{3 h}{h} - \frac{4}{h}

Cancel

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

= - \frac{3 x ^{2}}{h} - 6 x - 3 h + \frac{3 x}{h} + \frac{3 h}{h} - \frac{4}{h}

Cancel

\frac{3 h}{h} : 3

= - \frac{3 x ^{2}}{h} - 6 x - 3 h + \frac{3 x}{h} + 3 - \frac{4}{h}

\frac{k ^{a}}{n ( k ^{a} - n ^{a} )}

\frac{1}{( w i + 0.5 ) ^{2}}

(\frac{x}{2}) + 3

e^{x + 2} (2 x + 2)

\frac{( x + 5 )}{( x + 2 ) ( x + 3 ) ( x + 4 )}

What is expand (-3(x+h)^2+3(x+h)-4)/h ?
The solution to expand (-3(x+h)^2+3(x+h)-4)/h is -(3x^2)/h-6x-3h+(3x)/h+3-4/h