Find the range of the following function Find the range of the following function:
$$f(x)=\frac{x-1}{x^2-5x-6}$$
I know how to find the domain only
Please provide an explanation.
EDIT: Another question: find the range of
$$f(x)=\frac{1}{(1-x)(5-x)}$$
How would we do that?

From partial fractions decomposition,
$$\frac{x-1}{x^2-5x-6}=\frac{x-1}{(x+1)(x-6)} =\frac{2}{7(x+1)}+\frac{5}{7(x-6)}.$$
Both fractions are decreasing continuous functions on the domain: $(-\infty,-1)\cup (-1,6)\cup (6,+\infty)$. 
In particular, it is continuous decreasing on $(-1,6)$. On another hand, $$\lim_{x\to -1_+}f(x)=+\infty, \quad\lim_{x\to 6_-}f(x)=-\infty, $$
Hence, by the intermediate value theorem, the range of $f$ is $(-\infty,+\infty)$
