Does the following equation (sqrt(x+h)-sqrt(x))/h reduce to this equation 1/(sqrt(x+h)+sqrt(x)) and if so how?

Question

debbieg · Answer

you have 

$\large \dfrac{\sqrt{(x+h)}-\sqrt{x}}{h}$ 

and you are trying to determine if it is equivalent to 

$\large \dfrac{1}{\sqrt{(x+h)}+\sqrt{x}}$

right?

anonymous · Answer

Yes

phi · Answer

use the idea  (a-b)(a+b)=  a^2 - b^2

debbieg · Answer

ok, what would you have to multiple the den'r of the 1st equation by, in order to produce the den'r of the second equation?

debbieg · Answer

*multiply

debbieg · Answer

Remember, you can always multiply by a/a right? So figure out what you would need to multiply by in the den'r to get the den'r you want. Use that in a/a, e.g., multiply the whole thing by 1 but write 1 so that you "force" the required den'r. Then see what happens in the num'r.

If you can multiply by 1, and get the 2nd expression as the result, then the answer is yes. :)

debbieg · Answer

And as @phi  said, you will see that you will use that special product along the way. :)

anonymous · Answer

$$multiply the numerator and denominator by \sqrt{x+h}+\sqrt{x}   $$