jmc

The denominator can be simplified a bit to make this easier to calculate:

$$\begin{array}{rl}\frac{11!}{9!+2\cdot 8!}& =\frac{11!}{9\cdot 8!+2\cdot 8!}\\ & =\frac{11!}{11\cdot 8!}\\ & =\frac{10!}{8!}\\ & =10\cdot 9\\ & =\boxed{90}\end{array}$$