How do I find range of this function?

Question

How do I find range of-

$$y=\frac{\sqrt{x+7}-4}{x-9}$$

I think the traditional way of differentiating, finding critical points etc will be too hectic.

How do I do this?

Answer 1

Write your function in the form $$y=\frac{(\sqrt{x+7}-4)(\sqrt{x+7}+4)}{(x-9)(\sqrt{x+7}+4)}$$