How do I rationalize and simplify this?

Question

(x—9) / (√x + 3) 

Answer 1

MULTIPLY both top & bottom by the conjugate of the denominator, i.e. by (√x - 3). This will rationalize the denominator. Then you will have to simplify because you will seee that the (x-9)'s will cancel.

 

Alternatively, you can factor the numerator!  It equals (√x - 3)(√x + 3) and in this approach, the latter factor will be canceled by the denominator.  Same answer is obtained by either method.