Factoring (sqrt(x-5)-2)/(x-9): find limit as x goes to 9

[Placidius]

(sqrt(x-5)-2)/(x-9) ................. Those ()are super-important

Sorry, I don't know how write equations here. What I want to do is find the limit of this (as x goes to 9), but I posted it in algebra because really the problem is that I don't know how to get x-9 out of the denominator. I've tried multiplying by the conjugate on the top and factoring the bottom as though it were a difference of squares. It all just ends up a mess.

 

[tkhunny]

(sqrt(x-5)-2)/x-9

I've tried multiplying by the conjugate on the top

Please demonstrate: \(\displaystyle \dfrac{\sqrt{x-5} - 2}{x-9}\cdot\dfrac{\sqrt{x-5} + 2}{\sqrt{x-5} + 2}\)