how to simplify this$$\sqrt{x+h}-\sqrt{x} \over h$$ = $$1 \over \sqrt{x+h}+\sqrt{x}$$

Question

anonymous · Answer

multiply the top and bottom by (sqrt(x+4)+sqrt(x).
This will have the effect of removing the sqrt signs on top originally, and the x's will cancel just leaving an h which cancels with the h on bottom.  We're left only with the thing we originally multiplied by bottom and nothing on top

anonymous · Answer

top and bottom of both fractions?

dumbcow · Answer

im guessing you will be taking the limit as h->0

anonymous · Answer

i have to show how they are equivalent

dumbcow · Answer

yeah do what he said...multiply top and bottom by the conjugate and that will eliminate the radicals on top

anonymous · Answer

take the first and do what I said, you will reach the second.

anonymous · Answer

I understand..thanks! the only thing is what did you mean by: We're left only with the thing we originally multiplied by bottom and nothing on top

anonymous · Answer

multiplied by on bottom i meant