how to manipulate this expression...

[Guest]

I eventually need to take the limit as h->0 but i'm stuck here, unable to manipulate the expression further...

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

thanks!

 

[Unco]

The numerator:

\(\displaystyle \mbox{ \frac{1}{(x + h)^2} - \frac{1}{x^2}}\)

Subtract fractions (by cross-multiplying); then expand parentheses to observe some simplification.

 

[tkhunny]

Of course, what is meant is:

Subtract fractions by finding and using a common denominator, like any other fraction subtraction.