Question

In the following exercises, determine the values for which the rational expression is undefined.

$$\begin{gathered} \left(a\right)\frac{4x^{2}y}{3y} \\ \left(b\right)\frac{3x-2}{2x+1} \\ \left(c\right)\frac{u-1}{u^2-3u-28} \end{gathered}$$

Short answer

The required values for which the given expressions are undefined,

$$\begin{gathered} \mathrm{Part}\left(\mathrm{a}\right)y=0 \\ \mathrm{Part}\left(\mathrm{b}\right)x=-\frac{1}{2} \\ \mathrm{Part}\left(\mathrm{c}\right)u=-4,7 \end{gathered}$$

Step-by-step solution

Part (a) Step 1. Given Information  

The given expressions are

$$\begin{gathered} \left(a\right)\frac{4x^{2}y}{3y} \\ \left(b\right)\frac{3x-2}{2x+1} \\ \left(c\right)\frac{u-1}{u^2-3u-28} \end{gathered}$$

Part (a) Step 2. Calculation  

Set the denominator equal to zero and solve for the variable to determine for which values the given expression is undefined.

$$\begin{gathered} 3y=0 \\ y=0 \end{gathered}$$

Part (b) Step 1. Calculation  

Set the denominator equal to zero and solve for the variable to determine for which values the given expression is undefined.

$$\begin{gathered} 2x+1=0 \\ 2x=-1 \\ x=-\frac{1}{2} \end{gathered}$$

Part(c) Step 1. Calculation  

Set the denominator equal to zero and solve for the variable to determine for which values the given expression is undefined.

$$\begin{gathered} u^2-3u-28=0 \\ {u}^2-7u+4u-28=0 \\ u(u-7)+4(u-7)=0 \\ (u+4)(u-7)=0 \\ u=-4,7 \end{gathered}$$