Question

Divide the rational expression$\frac{3{\mathrm{y}}^2-12\mathrm{y}-63}{4\mathrm{y}+3}÷(6{\mathrm{y}}^2-42\mathrm{y})$

Short answer

The value of the expression is$\frac{7}{2}.$

Step-by-step solution

Step 1. Given Information

Given that the expression is$\frac{3{\mathrm{y}}^2-12\mathrm{y}-63}{4\mathrm{y}+3}÷(6{\mathrm{y}}^2-42\mathrm{y})$and taken as$\frac{{\mathrm{y}}^2-8}{{\mathrm{y}}^2-\mathrm{y}-2}.$

Step 2. Simplification

It can be simplified as,

$$\begin{gathered} \frac{{\mathrm{y}}^2-8}{{\mathrm{y}}^2-\mathrm{y}-2},y=1 \\ =\frac{{\left(1\right)}^2-8}{{\left(1\right)}^2-1-2} \\ =\frac{-7}{-2} \\ =\frac{7}{2} \end{gathered}$$