How to Rationalize the Numerator in a Fraction?

[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. Homework 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.

 

[LCKurtz]

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

 

[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.

 

[Nitrate]

Alright, I got it guys!
Thanks :)