Early Calculus A/B HW prob. with limits

[Cambelljose]

I might just be over thinking this problem but I don't get how lim _x->0 ((1/(h+x))-(1/h))/x = 1/h²​. Please help. ALSO LOOK BELOW

 

[Cambelljose]

To clarify - I know the answer i just need help on the computation.

 

[stapel]

I might just be over thinking this problem but I don't get how lim _x->0 ((1/(h+x))-(1/h))/x = 1/h²​.

I am understanding the expression on the left-hand side of the "equals" sign to be as follows:

. . . . .\(\displaystyle \displaystyle{\lim_{x\, \rightarrow\, 0}\, \frac{\left(\frac{1}{h\, +\, x}\, -\, \frac{1}{h}\right)}{x}}\)

Is this correct? If so, what did you get when you converted the subtraction in the "numerator" of the limit to a common denominator? What did you get when you did the subtraction? What did you get when you simplified the result? Then what did you get when you flipped the "x" in the "denominator", turning it into "1/x", and multiplied? Then what happened when you took the limit as x tends toward zero?

If not, kindly please reply with clarification and correction. Thank you!

 

[Cambelljose]

Thank you I got it. I don't know why but I always forget about common denominators. Thank you for the help.