SOLUTION: Hi, I'm supposed to simplify this if possible. ((1/(x+h)^2)-(1/x^2))/h I've tried several ways of solving this, most recently coming up with the answer (1-2xh-h^2)/(x^2h+2xh^2+h

Question 286253: Hi, I'm supposed to simplify this if possible.
((1/(x+h)^2)-(1/x^2))/h
I've tried several ways of solving this, most recently coming up with the answer (1-2xh-h^2)/(x^2h+2xh^2+h^3) but this isn't right. Can someone please help me?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
simplify this if possible.
((1/(x+h)^2)-(1/x^2))/h
-------------------
lcd = x^2(x+h)^2
Rewrite each fraction with the lcd as its denominator:
------------------------
[(x^2/lcd - (x+h)^2/lcd]/h
Combiine the numerators over the lcd:
---------------------
[x^2 -x^2-2hx-h^2]/(lcd*h)
Simplify the numerator:
-------------------------
(2hx-h^2)/(lcd*h)
Divide by "h" to get:
---
= (2x-h)/(x^2(x+h)^2)
---------------------------
Cheers,
Stan H.
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