Help! Suppose that (f(x+h)-f(x))/h = (-2h(x+4)-h^2)/h(x+h+4)^2(x+4)^2

Find the slope m of the tangent line at x+1.
m=?

Question

Help! Suppose that (f(x+h)-f(x))/h = (-2h(x+4)-h^2)/h(x+h+4)^2(x+4)^2    

Find the slope m of the tangent line at x+1. 
m=?

anonymous · Answer

at $x=1$ ?

anonymous · Answer

Yes sorry I typed it wrong

anonymous · Answer

replace $x$ by $1$ and compute the limit

anonymous · Answer

is it $$\frac{-2h(x+4)-h^2}{h(x+h+4)^2(x+4)^2} $$??

anonymous · Answer

Yes

anonymous · Answer

then start with 
$$\frac{-2h(1+4)-h^2}{h(1+h+4)^2(1+4)^2}$$

anonymous · Answer

$$\frac{-10h-h^2}{h(h+5)^2\times 25}$$

anonymous · Answer

I got that. Then I simplified the bottom.

anonymous · Answer

$$\frac{h(-10-h)}{25h(h+5)^2}=\frac{-10-h}{25(h+5)^2}$$ now replace $h$ by zero to get your answer

anonymous · Answer

don't multiply out, that is a bad idea
factor and cancel the $h$ so you can replace $h$ by $0$ without getting a zero in the denominator

anonymous · Answer

O ok.

anonymous · Answer

I got 
m= -10/625