Find Limit (3-sqrt(x+5))/(x-4), x->4, algebraically

[Dutch_Luck]

The question asks to find the limit as x approaches 4 of the following function;

(3-√(x+5))/(x-4)

I understand graphically that there is a removable discontinuity at x=4 and that a limit exists. I can't find a way algebraically to solve the problem. Could someone help me out or pointme in the right direction.

 

[galactus]

Multiply top and bottom by the conjugate of the numerator.

\(\displaystyle \L\\\lim_{x\to\4}\frac{(3-sqrt{x+5})}{(x-4)}\cdot\frac{(3+\sqrt{x+5})}{(3+\sqrt{x+5})}\)

Now, simplify. It should work nicely.

 

[Dutch_Luck]

Thanks, that worked good. I knew it was something to do with multiplying, except I just was thinking of simpler terms to multiply with.