# Homework Help: Rationalizing a numerator

1. Sep 11, 2011

### Nitrate

1.
Haven't done this type of math in a long time, here's the question:
1. Rationalize the numerator
a) (√x - 3) / (x - 9)

Can't get the answer for the life of me. The textbook says (1)/(√x - 3)

the / dictates division.

2. Relevant equations
Question: (√x - 3) / (x - 9)
Answer: (1)/(√x - 3)

3. The attempt at a solution

I multiplied the top and bottom by the conjugate of the numerator (√x + 3)
and ended up getting (x-9)/(x√x + 3x - 9√x - 27)

and I get stumped here.

2. Sep 11, 2011

### LCKurtz

Instead of multiplying the denominator out like that, leave it factored and see if you can cancel factors.

3. Sep 11, 2011

### symbolipoint

From here, which looks good, (x-9)/(x√x + 3x - 9√x - 27)
= $\frac{x-9}{\sqrt{x}(x-9)+3(x-9}$
= $\frac{x-9}{(x-9)(\sqrt{x}-3)}$
... can then be simplified.

4. Sep 11, 2011

### Nitrate

Alright, I got it guys!
Thanks :)