Question

Divide$\frac{{\mathrm{x}}^2-4\mathrm{x}-12}{{\mathrm{x}}^2+8\mathrm{x}+12}÷\frac{{\mathrm{x}}^2-36}{3\mathrm{x}}$

Short answer

The rational factor is undefined if$\mathrm{u}=6,\mathrm{u}=-5.$

Step-by-step solution

Step 1. Given information

Given that the rational expression is$\frac{{\mathrm{x}}^2-4\mathrm{x}-12}{{\mathrm{x}}^2+8\mathrm{x}+12}÷\frac{{\mathrm{x}}^2-36}{3\mathrm{x}}$and taken as$\frac{\mathrm{u}-3}{{\mathrm{u}}^2-\mathrm{u}-30}.$

Step 2. Simplification

There is an undefined expression when the denominator will equal to zero.

$$\begin{gathered} {\mathrm{u}}^2-\mathrm{u}-30=0 \\ {\mathrm{u}}^2-6\mathrm{u}+5\mathrm{u}-30=0 \\ \mathrm{u}(\mathrm{u}-6)+5(\mathrm{u}-6)=0 \\ (\mathrm{u}-6)(\mathrm{u}+5)=0 \\ \mathbf{u}\mathbf{=}\mathbf{6}\mathbf{,}\mathbf{u}\mathbf{=}\mathbf{-}\mathbf{5} \end{gathered}$$