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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

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

Cancel

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

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

d y - (y - 8)^{2} d x

(x + 3) (x + 4 = 0)

\frac{9}{( 3 x - 1 ) ( 3 x + 5 )}

ln (x) (6 x + 1)

\frac{b ( 1 + 1.1 r )}{1 - 1.1 r}

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