Derivatives

[Johnmoon]

Can't seem to figure out what the fraction becomes after it's reduced. Please help.

 

[Steven G]

Can you show us your attempt? You need to just get a common denominator.
To do well in calculus you MUST know your algebra!

 

[pka]

View attachment 12602
Can't seem to figure out what the fraction becomes after it's reduced. Please help.

\(\displaystyle \begin{align*}\frac{f(x+h)-f(x)}{h}&=\frac{\frac{4}{x+h-8}-\frac{4}{x-8}}{h} \\&=\frac{4(x-8)-4(x+h-8)}{h(x+h-8)(x-8)}\\&=\frac{-4h}{h(x+h-8)(x-8)} \\&=\frac{4(x-8)-4(x+h-8)}{h(x+h-8)(x-8)}\\&=\frac{-4}{(x+h-8)(x-8)}\end{align*}\)
If \(\displaystyle h\to 0\) what is \(\displaystyle f'(x)~?\)