Answer
$\frac{11}{7k-15}, with$ $k\ne\frac{15}{7}$
Work Step by Step
Given : $\frac{11k+121}{7k-15} \div (k+11)$
This becomes : $\frac{11(k+11)}{7k-15} \times \frac{1}{k+11}$
$= \frac{11(k+11)}{7k-15} \times \frac{1}{k+11}= \frac{11}{7k-15} $
(After dividing out the common factor (k+11))
