Question

For what values of the variable is the rational expression undefined? $$\frac{4}{x^{2}-1}$$

Short answer

The values of x for which the rational expression \( \frac{4}{x^{2}-1} \) is undefined are \( x = 1 \) and \( x = -1 \).

Step-by-step solution

Identify the Denominator

The denominator of the given rational expression: \( \frac{4}{x^{2}-1} \) is \( x^{2}-1 \). This expression will be undefined when its denominator is zero.

Set the Denominator Equal to Zero

To find the roots of the denominator, set \( x^{2}-1 = 0 \). This will give the values of \( x \) for which the rational expression is undefined.

Solve the Equation

Solving the equation \( x^{2}-1 = 0 \), we get \( x^{2} = 1 \). Thus, \( x = \sqrt{1} \) & \( x = -\sqrt{1} \) Hence, \( x = 1 \) & \( x = -1 \).