Simplifying a complex rational

I am having a rather frustrating time simplifying this expression...

{[1/(x+h)^2]-[1/x^2]}/h

my first step as instructed by my pre-calculus textbook is to multiply [x^2(x+h)^2] to both the numerator and denominator as a result I see:

{[x^2(x+h)^2]/(x+h)^2}-[x^2(x+h)^2]/x^2

I think my treatment of fractions is the problem because my next action is to eliminate (x+h)^2 from the num. and denom. of the left expression and x ^2 from the num. and denom. of the right expression leaving me with:

[x^2-(x+h)^2]/[hx^2(x+h)^2]

this is my dead end and I know that the only reason I am here is because I cannot see past the error in my mind, please help me.