Factoring Derivatives Using Limits: 4/x^2

[lax1113]

Homework Statement

lim {f(x+h)-f(x)}/h
f(x)=4/x







So far, i have plugged in the function, and got
{4/(x+h)-(4/x)}/h

I have a Ti-89, my brother no longer needed for college, and when i factored this, it gave me -4/x^2. This is also the answer supplied in the back of the book. With that being said, i have the answer for this worksheet, but i really want to know HOW to factor this. I know it is going to be showing up a whole heck of alot, with this being the definition of a derivative using limits, so i want to know how this factors. I have tried a few times, but due to the difficulty of writing math by typing, i will just say that all attempts ended in indeterminant answers, so obviously, something hasn't worked.

 

[Defennder]

What have you done so far? You plugged in the function correctly. Now just combine everything into 1 common fraction and simplify it. Then note that (x+h) approaches x when h approaches 0.