Question

Rationalize the numerator:

Answer 1

\[(\sqrt{x} - \sqrt{x+h}) / h \]

Answer 2

multiply top and bottom by conjugate of top

Answer 3

I understand how to do it. You get -1 for the top, but not sure of the bottom.

Answer 4

\[\frac{\sqrt{x}-\sqrt{x+h}}{h} \cdot \frac{\sqrt{x}+\sqrt{x+h}}{\sqrt{x}+\sqrt{x+h}}\]

Answer 5

you get -1 on top before or after canceling common factors after the multiplication part

Answer 6

and that was a question

Answer 7

I know the answer for the bottom is \[\sqrt{x} + \sqrt{x+h}\] but how do you get that with the multiplied h?

Answer 8

\[\frac{(x)-(x+h)}{h(\sqrt{x}+\sqrt{x+h})}\]
you do understand we have -h/h=-1 right?

Answer 9

Yes

Answer 10

so what is the question exactly

Answer 11

How does it work out for the bottom?

Answer 12

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

Answer 13

sqrt(x)+sqrt(x+h) on the bottom*

Answer 14

\[\frac{(x)-(x+h)}{h(\sqrt{x}+\sqrt{x+h})}=\frac{-h}{h} \frac{1}{\sqrt{x}+\sqrt{x+h}}\]