Question

Determine the values for which the rational expression is undefined.

$\frac{5{\mathrm{x}}^2{\mathrm{y}}^2}{8\mathrm{y}}$

Short answer

Rational function can be undefined when$\mathrm{y}=0.$

Step-by-step solution

Step 1. Given Data

Rational function can be given as$\mathrm{R}\left(\mathrm{x}\right)=\frac{5{\mathrm{x}}^2{\mathrm{y}}^2}{8\mathrm{y}}.$

Step 2. Critical point

To find the critical point,

$$\begin{gathered} 5{\mathrm{x}}^2{\mathrm{y}}^2=0 \\ \mathrm{x}=0,\mathrm{y}=0 \\ 8\mathrm{y}=0 \\ \mathrm{y}=0 \end{gathered}$$

Using critical points, the points can be substituted to find point when rational function is undefined. At y=0,

$\mathrm{R}\left(\mathrm{x}\right)=\frac{0}{0}=\infty$

The function is undefined at y=0.