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We have to determine the values for which the rational expression is undefined:

$鈸�\frac{4p}{5q}鈸�\frac{y鈭�1}{3y+2}鈸�\frac{m鈭�5}{m^2+m鈭�6}$

The expression will be undefined when the denominator is zero.

Set the denominator equal to zero. Solve for the variable.

$$\begin{gathered} 5q=0 \\ q=0 \end{gathered}$$

$\mathrm{The}\mathrm{rational}\mathrm{expression}\frac{4p}{5q}\mathrm{is}\mathrm{undefined}\mathrm{for}q=0.$

The expression will be undefined when the denominator is zero.

Set the denominator equal to zero. Solve for the variable.

$$\begin{gathered} 3y+2=0 \\ 3y+2-2=0-2 \\ 3y=-2 \\ \frac{3}{3}y=-\frac{2}{3} \\ y=-\frac{2}{3} \end{gathered}$$

$\mathrm{The}\mathrm{rational}\mathrm{expression}\frac{y鈭�1}{3y+2}\mathrm{is}\mathrm{undefined}\mathrm{for}y=-\frac{2}{3}.$

The expression will be undefined when the denominator is zero.

Set the denominator equal to zero. Solve for the variable.

$$\begin{gathered} m^2+m鈭�6=0 \\ {m}^2+(3-2)m鈭�6=0 \\ {m}^2+3m-2m鈭�6=0 \\ m(m+3)-2(m+3)=0 \\ (m-2)(m+3)=0 \\ m-2=0\mathrm{or}\mathrm{m}+3=0 \\ m=2\mathrm{or}\mathrm{m}=-3 \end{gathered}$$

$\mathrm{The}\mathrm{rational}\mathrm{expression}\frac{m鈭�5}{m^2+m鈭�6}\mathrm{is}\mathrm{undefined}\mathrm{for}m=2\mathrm{and}m=-3.$