Q1. - Algebra 1

Question

What are the excluded values of the variable in the expression $\frac{{\mathbf{x}}^2\mathbf{-}\mathbf{x}\mathbf{-}\mathbf{12}}{{\mathbf{x}}^2\mathbf{-}\mathbf{x}\mathbf{-}\mathbf{2}}$?

Step-by-Step Solution

Answer

Excluded values of the variable in the expression are $-\mathbf{1}$ and $\mathbf{2}$.

Step 1. Exclude the values.

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

 $\begin{array}{c}{x}^2-x-2=0\\ (x+1)(x-2)=0\end{array}$

Step 2. Zero product property.

Apply zero product property to above equation.

 $\begin{array}{l}x+1=0\text{ or }x-2=0\\ x=-1\text{ x}=2\end{array}$

Step 3. Write a conclusion.

Division by zero is undefined. The values $x=-1$ and $x=2$, results in zero of the denominator of an original expression. Therefore, $x=-1$ and $x=2$ are excluded values.