## anonymous one year ago Rationalize the numerator:

1. anonymous

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

2. freckles

multiply top and bottom by conjugate of top

3. anonymous

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

4. freckles

$\frac{\sqrt{x}-\sqrt{x+h}}{h} \cdot \frac{\sqrt{x}+\sqrt{x+h}}{\sqrt{x}+\sqrt{x+h}}$

5. freckles

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

6. freckles

and that was a question

7. anonymous

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

8. freckles

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

9. anonymous

Yes

10. freckles

so what is the question exactly

11. anonymous

How does it work out for the bottom?

12. 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

13. freckles

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

14. freckles

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