Rationalize the numerator of:

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

I got:
1/ (((x^2+xh)^(1/2))+((x^3+2x^2h+xh^2)^(1/2)))

But am really unsure about the denominator...

Question

Rationalize the numerator of:

(((x)^(1/2))-((x+h)^(1/2)))/(h((x)^(1/2))((x+h)^(1/2))

I got:
1/ (((x^2+xh)^(1/2))+((x^3+2x^2h+xh^2)^(1/2)))

But am really unsure about the denominator...

anonymous · Answer

my eyes!!!  too many parenthesisesess.

anonymous · Answer

$$(\sqrt{x}-\sqrt{x+h})/(h \sqrt{x}\sqrt{x+h})$$

anonymous · Answer

i'm kidding... dont need to...

anonymous · Answer

Sorry am clearing it up now that is the question...

anonymous · Answer

Oh okay, lol... is that the same answer that you got?

anonymous · Answer

$$1/ (\sqrt{x^2+xh}+\sqrt{x^3+2x^2h+xh^2}) $$

anonymous · Answer

just to clear it up..
$$\large \frac {\sqrt{x}-\sqrt{x+h}}{h \sqrt {x} \sqrt{x+h}}$$

anonymous · Answer

shouldn't that be a -1 at the top?

anonymous · Answer

yes in the answer...

anonymous · Answer

still doing it... hang on..

anonymous · Answer

okay :)

dumbcow · Answer

yeah you should get
$$\frac{-1}{\sqrt{x}\sqrt{x+h}(\sqrt{x}+\sqrt{x+h})} = \frac{-1}{x \sqrt{x+h} + (x+h)\sqrt{x}}$$

anonymous · Answer

i left it in factored form (the denominator):
h*sqrt(x(x+h)) * (sqrt(x+h)+sqrt(x))

anonymous · Answer

talk about parenthesisises.

anonymous · Answer

how'd you get rid of the h if you left it factored

anonymous · Answer

is it okay for me to expand it that way?