Question

State the excluded value or values for each function.

$y=\frac{5}{x^2-5x-24}$

Short answer

Excluded values of the function are$8$ and $-3$.

Step-by-step solution

Step 1. Exclude the values.

Exclude the values for which$x^2-5x-24$ equals 0.

$\begin{array}{c}{x}^2-5x-24=0\\ \left(x+3\right)\left(x-8\right)=0\end{array}$

Step 2. Zero product property.

If$xy=0$ then, either$x=0$ or $y=0$.

Step 3. Zero product property.

Apply zero product property to above equation.

$$\begin{gathered} x+3=0\text{or}x-8=0 \\ x=-3x=8 \end{gathered}$$

Therefore,$x\ne -3$ and $x\ne 8$.