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

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

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

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

\frac{g h}{h} : g

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

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

(t - 3) H (t - 3)

3 (\frac{1}{5} x + \frac{2}{5} y)

\frac{\partial}{\partial x} ((z) ((8 x + 2 y)^{4}))

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