You can factor both the numerator and denominator:
[tex] \frac{x^2 -10x-11}{x^2 - 121} = \frac{(x-11)(x+1)}{(x-11)(x+11)} [/tex]
Next, cancel out common factors:
[tex]\frac{(x-11)(x+1)}{(x-11)(x+11)} = \frac{x+1}{x+11}[/tex]
Your answer should be [tex] \frac{x+1}{x+11}[/tex].
