anonymous
  • anonymous
Rationalize the numerator:
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[(\sqrt{x} - \sqrt{x+h}) / h \]
freckles
  • freckles
multiply top and bottom by conjugate of top
anonymous
  • anonymous
I understand how to do it. You get -1 for the top, but not sure of the bottom.

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freckles
  • freckles
\[\frac{\sqrt{x}-\sqrt{x+h}}{h} \cdot \frac{\sqrt{x}+\sqrt{x+h}}{\sqrt{x}+\sqrt{x+h}}\]
freckles
  • freckles
you get -1 on top before or after canceling common factors after the multiplication part
freckles
  • freckles
and that was a question
anonymous
  • anonymous
I know the answer for the bottom is \[\sqrt{x} + \sqrt{x+h}\] but how do you get that with the multiplied h?
freckles
  • freckles
\[\frac{(x)-(x+h)}{h(\sqrt{x}+\sqrt{x+h})}\] you do understand we have -h/h=-1 right?
anonymous
  • anonymous
Yes
freckles
  • freckles
so what is the question exactly
anonymous
  • anonymous
How does it work out for the bottom?
freckles
  • freckles
after using -h/h=-1 you are left with sqrt(x)+sqrt(x+h) there is nothing else to do unless you have a limit question here
freckles
  • freckles
sqrt(x)+sqrt(x+h) on the bottom*
freckles
  • freckles
\[\frac{(x)-(x+h)}{h(\sqrt{x}+\sqrt{x+h})}=\frac{-h}{h} \frac{1}{\sqrt{x}+\sqrt{x+h}}\]

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