# Homework Help: Rationalizing denominator

1. Feb 9, 2008

### temaire

1. The problem statement, all variables and given/known data
Rationalize the denominator and simplify:

$$\frac{x^2-9}{\sqrt{3-x}}$$

2. Relevant equations
None.

3. The attempt at a solution
The answer to the question is $$-(x+3)\sqrt{3-x}$$, but this is what I'am getting:
Can someone show me where I went wrong?

Last edited by a moderator: May 3, 2017
2. Feb 9, 2008

### rocomath

Well, when you rationalize a problem. You want to get rid of the radical. In order for the radical to go away, you have to manipulate it so that the power is 1.

You multiplied the both numerator and denominator by $$\sqrt{3+x}$$ when you should have multiplied both by $$\sqrt{3-x}$$

3. Feb 9, 2008

### temaire

But I thought that when you rationalize, you're supposed to multiply the numerator and denominator by the conjugate.

4. Feb 9, 2008

### Gib Z

Since we have a square root, it's like a grouping symbol, we have to take the entire piece as one single thing. So we we let $\sqrt{3+x} = a$, then theres really only one thing in the denominator. We only multiply by the conjugate when the identity $p^2-q^2 = (p+q)(p-q)$ is useful to us, in this case not. This time it was easier just to get rid of the square root.

Or another way to think of it, you have a+0 in the denominator, you have to multiply by its conjugate, a-0 = a.

5. Feb 10, 2008

### HallsofIvy

Yes, and what is the conjugate here? The conjugate of $a+ b\sqrt{c}$ is $a- b\sqrt{c}$. What are a, b, and c here?