Question

1 Let f(x) Expand and simplify: 2x - 9 f(x + h) - f(x) h - (Enter your answer in reduced form)

Answer 1

Solution

We have the following function given:

$f(x)=\frac{1}{2x-9}$

and we want to find:

$\frac{f(x+h)-f(x)}{h}$

Replacing we have:

$\frac{\frac{1}{2(x+h)-9}-\frac{1}{2x-9}}{h}=\frac{\frac{2x-9-2x-2h+9}{(2(x+h)-9)(2x-9)}}{h}$

And if we simplify we got:

$\frac{-2h}{h\lbrack(2x+2h-9)(2x-9)\rbrack}=\frac{-2}{(2(x+h)-9)(2x-9)}$