Question

Divide$\frac{{\mathrm{y}}^2-16}{4}÷\frac{{\mathrm{y}}^3-64}{2{\mathrm{y}}^2+8\mathrm{y}+32}$

Short answer

The value of expression is$\frac{-5}{6}.$

Step-by-step solution

Step 1. Given Information

Given that the expression is $\frac{{\mathrm{y}}^2-16}{4}÷\frac{{\mathrm{y}}^3-64}{2{\mathrm{y}}^2+8\mathrm{y}+32}$and rational expression is$\frac{4\mathrm{p}-1}{{\mathrm{p}}^2+5}.$

Step 2. Substitution

On substituting,

$$\begin{gathered} \frac{4\mathrm{p}-1}{{\mathrm{p}}^2+5},\mathrm{p}=-1 \\ =\frac{4\times 1-1}{{(-1)}^2+5} \\ =\frac{\mathbf{-}\mathbf{5}}{\mathbf{6}} \end{gathered}$$