Question

Determine the values for which the rational expression is undefined.

$\frac{5\mathrm{a}+3}{3\mathrm{a}-2}$

Short answer

when$\mathrm{a}=\frac{2}{3}$, rational function is undefined.

Step-by-step solution

Step 1. Given data

Given that the rational expression is$\frac{5\mathrm{a}+3}{3\mathrm{a}-2}.$

Step 2. Calculation

When the denominator of rational function is zero, then the rational function will be undefined.

$$\begin{gathered} (3\mathrm{a}-2)=0 \\ \mathrm{a}=\frac{2}{3} \\ \mathrm{At}\mathrm{a}=\left(\frac{2}{3}\right) \\ \mathrm{R}\left(\mathrm{x}\right)=\frac{5\left({\displaystyle \frac{2}{3}}\right)+3}{3\left({\displaystyle \frac{2}{3}}\right)-2} \\ \mathrm{R}\left(\mathrm{x}\right)=\frac{\left({\displaystyle \frac{10}{3}}\right)+3}{2-2} \\ \mathrm{R}\left(\mathrm{x}\right)=\infty \end{gathered}$$