Q. 2 - Intermediate Algebra

Question

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

$$\begin{gathered} \left(\text{a}\right)\frac{10m}{11n} \\ \left(\text{b}\right)\frac{6y+13}{4y-9} \\ \left(\text{c}\right)\frac{b-8}{b^2-36} \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} \left(\text{a}\right)\frac{10m}{11n}\text{ is undefined at }n=0 \\ \left(\text{b}\right)\frac{6y+13}{4y-9} \mathrm{is} \mathrm{undefined} \mathrm{at} y=\frac{9}{4} \\ \left(\text{c}\right)\frac{b-8}{b^2-36} \mathrm{is} \mathrm{undefined} \mathrm{at} b=-6,6 \end{gathered}$$

Step 1 . Given information

$$\begin{gathered} \left(\text{a}\right)\frac{10m}{11n} \\ \left(\text{b}\right)\frac{6y+13}{4y-9} \\ \left(\text{c}\right)\frac{b-8}{b^2-36} \end{gathered}$$

Part a . step 1 . find the undefined values

$\left(\text{a}\right)\frac{10m}{11n}$

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

$$\begin{gathered} 11n=0 \\ n=0 \end{gathered}$$

Hence, the undefined value at $n=0.$

Part b . step 1 . find the undefined values

$\left(\text{b}\right)\frac{6y+13}{4y-9}$

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

$$\begin{gathered} 4y-9=0 \\ 4y=9 \\ y=\frac{9}{4} \end{gathered}$$

Hence, the undefined value at $y=\frac{9}{4}.$

Part c . step 1 . find the undefined values

$\left(\text{c}\right)\frac{b-8}{b^2-36}$

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

$$\begin{gathered} b^2-36=0 \\ {b}^2=36 \\ b=\pm 6 \end{gathered}$$

Hence, the undefined values are at $b=-6,6.$