Q. 4 - Intermediate Algebra

Question

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

$$\begin{gathered} \left(\text{a}\right)\frac{5p{q}^2}{9q} \\ \left(\text{b}\right)\frac{7a-4}{3a+5} \\ \left(\text{c}\right)\frac{1}{x^2-4} \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} \left(\text{a}\right)\frac{5p{q}^2}{9q}\text{undefinend at }q=0 \\ \left(\text{b}\right)\frac{7a-4}{3a+5}\text{undefined at }a=-\frac{5}{3} \\ \left(\text{c}\right)\frac{1}{x^2-4}\text{undefined at} x=-2,2. \end{gathered}$$

Step 1 . Given information

$$\begin{gathered} \left(\text{a}\right)\frac{5p{q}^2}{9q} \\ \left(\text{b}\right)\frac{7a-4}{3a+5} \\ \left(\text{c}\right)\frac{1}{x^2-4} \end{gathered}$$

Part a . step 1 . find the undefined values

$\left(\text{a}\right)\frac{5p{q}^2}{9q}$

Equate the denominator to zero and solve for the unknown variable.  

$$\begin{gathered} 9q=0 \\ q=0 \end{gathered}$$

Hence, the undefined value at  $q=0.$

Part b . step 1 . find the undefined values

$\left(\text{b}\right)\frac{7a-4}{3a+5}$

Equate the denominator to zero and solve for the unknown variable.  

$$\begin{gathered} 3a+5=0 \\ 3a=-5 \\ a=-\frac{5}{3} \end{gathered}$$

Hence, the undefined value at  $a=-\frac{5}{3}.$

Part c . step 1 . find the undefined values

$\left(\text{c}\right)\frac{1}{x^2-4}$

Equate the denominator to zero and solve for the unknown variable.  

$$\begin{gathered} x^2-4=0 \\ {x}^2=4 \\ x=\pm 2 \end{gathered}$$

Hence, the undefined value at  $x=-2,2.$