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

The solution to expand (g(x+h)^2-g(x))/h is (gx^2)/h+2gx+gh-(gx)/h

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

expand

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

\frac{g x ^{2}}{h} + 2 gx + g h - \frac{gx}{h}

Solution steps

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

Remove parentheses:

(a) = a

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

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

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

Expand

g (x^{2} + 2 x h + h^{2}) - gx : g x^{2} + 2 gx h + g h^{2} - gx

= \frac{g x ^{2} + 2 gx h + g h ^{2} - gx}{h}

Apply the fraction rule:

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

\frac{g x ^{2} + 2 gx h + g h ^{2} - gx}{h} = \frac{g x ^{2}}{h} + \frac{2 gx h}{h} + \frac{g h ^{2}}{h} - \frac{gx}{h}

= \frac{g x ^{2}}{h} + \frac{2 gx h}{h} + \frac{g h ^{2}}{h} - \frac{gx}{h}

Cancel

\frac{2 gx h}{h} : 2 gx

= \frac{g x ^{2}}{h} + 2 gx + \frac{g h ^{2}}{h} - \frac{gx}{h}

Cancel

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

= \frac{g x ^{2}}{h} + 2 gx + g h - \frac{gx}{h}

\frac{1 - cos ( 5 x - 5 )}{( x - 1 ) ^{2}}

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

\frac{( x + 1 ) ( x - 5 )}{( x + 3 ) ( x - 6 )}

(8 x^{2} - 2 x y + 3) d x

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

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