Question

Identify all of the values of $y$ for which the expression $\frac{y-4}{y^2-4y-12}$ is undefined.

$\left(A\right)-2,4,6\left(B\right)-6,-4,2\left(C\right)-2,0,6\left(D\right)-2,6$

Short answer

The expression is undefined for $y=-2,6$. So, option (D) is correct.

Step-by-step solution

Step 1. Write down the given information.

The given expression is $\frac{y-4}{y^2-4y-12}$.

Step 2. Concept used.

The expression will be undefined for which the denominator of the given expression will be equal to zero.

Step 3. Calculation.

The given expression $\frac{y-4}{y^2-4y-12}$has denominator $y^2-4y-12$. Therefore, equating $y^2-4y-12=0$gives,

$\begin{array}{l}{y}^2-4y-12=0\\ \left(y-6\right)\left(y+2\right)=0\\ y+2=0\text{\hspace{0.33em}or}y-6=0\\ y=-2\text{\hspace{0.33em}or}y=6\\ y=\left\{-2,6\right\}\\ y=-2,6\end{array}$

Since the expression is undefined for $y=-2,6$. So, option (D) is correct.

Step 4. Conclusion.

The expression is undefined for $y=-2,6$. So, option (D) is correct.