Question

Determine the value for which each rational expression is undefined.

$$\begin{gathered} \left(\text{a}\right)\frac{3y^2}{8x} \\ \left(\text{b}\right)\frac{8n-5}{3n+1} \\ \left(\text{c}\right)\frac{a+10}{a^2+4a+3} \end{gathered}$$

Short answer

$\left(\text{a}\right)\frac{3y^2}{8x}$is undefined at $x=0.$

$\left(\text{b}\right)\frac{8n-5}{3n+1}$is undefined at$n=-\frac{1}{3}.$

$\left(\text{c}\right)\frac{a+10}{a^2+4a+3}$is undefined at

$a=-3\text{or}a=-1$

Step-by-step solution

Step 1. Given information

The given rational expressions are

$$\begin{gathered} \left(\text{a}\right)\frac{3y^2}{8x} \\ \left(\text{b}\right)\frac{8n-5}{3n+1} \\ \left(\text{c}\right)\frac{a+10}{a^2+4a+3} \end{gathered}$$

Part a. Step 1. Find the undefined values

$\left(\text{a}\right)\frac{3y^2}{8x}$

Set the denominator equal to zero and solve the equation

$8x=0$

$x=0$

Hence, the given rational expression is undefined at$x=0.$

Part b. Step 1.Find the undefined values

$\left(\text{b}\right)\frac{8n-5}{3n+1}$

Set the denominator equal to zero and solve the equation

$$\begin{gathered} 3n+1=0 \\ 3n=-1 \\ n=-\frac{1}{3} \end{gathered}$$

Hence, the given rational expression is undefined atlocalid="1644829474496" $n=-\frac{1}{3}.$

Part c. Step1. Find the undefined values

$\left(\text{c}\right)\frac{a+10}{a^2+4a+3}$

Set the denominator equal to zero and solve the equation

$$\begin{gathered} a^2+4a+3=0 \\ {a}^2+3a+a+3=0 \\ a(a+3)+(a+3)=0 \\ \left(a+3\right)\left(a+1\right)=0 \\ \left(a+3\right)=0\text{or}\left(a+1\right)=0 \\ a=-3\text{or}a=-1 \end{gathered}$$

Hence, the given rational expression is undefined at$a=-3\text{or}a=-1.$