Answer
$\frac{1}{x+1}, with$ $x\ne-1$
Work Step by Step
Given : $\frac{x^{2}+10x-11}{x^{2}+12x+11} \div (x-1)$
This becomes : $\frac{(x-1)(x+11)}{(x+1)(x+11)} \times \frac{1}{x-1}$
$= \frac{(x-1)(x+11)}{(x+1)(x+11)} \times \frac{1}{x-1}= \frac{1}{x+1} $
(After dividing out the common factors (x-1) and (x+11))
