Question

Divide$\frac{11+\mathrm{w}}{\mathrm{w}-9}÷\frac{121-{\mathrm{w}}^2}{9-\mathrm{w}}$

Short answer

The value of the expression is$\frac{22}{5}.$

Step-by-step solution

Step 1. Given data

Given that the expression is$\frac{11+\mathrm{w}}{\mathrm{w}-9}÷\frac{121-{\mathrm{w}}^2}{9-\mathrm{w}}$and taken as$\frac{{\mathrm{q}}^2-5}{\mathrm{q}+3}.$

Step 2. Simplification

On substituting,

$$\begin{gathered} =\frac{7^2-5}{7+3} \\ =\frac{44}{10} \\ =\frac{22}{5} \end{gathered}$$