Q50. - Algebra 2

Question

For what values of $x$ is the expression $\frac{4x}{x^2-x}$ undefined.

$\left(A\right)-1,1 \left(B\right)-1,0,1 \left(C\right)0,1 \left(D\right)0 \left(E\right)1,2$

Step-by-Step Solution

Answer

The expression is undefined for $x=0,1$. So, option (C) is correct.

Step 1. Write down the given information.

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

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 $\frac{4x}{x^2-x}$ has denominator $x^2-x$. Therefore, equating $x^2-x=0$ gives,

$\begin{array}{l}{x}^2-x=0\\ x\left(x-1\right)=0\\ x=0\text{\hspace{0.33em}or }x-1=0\\ x=0\text{\hspace{0.33em}or }x=1\\ x=\left\{0,1\right\}\\ x=0,1\end{array}$

Since the expression is undefined for $x=0,1$. So, option (C) is correct.

Step 4. Conclusion.

The expression is undefined for $x=0,1$. So, option (C) is correct.