Problem 94 - Introductory Algebra for College Students

Question

Explain how to find the number or numbers, if any, for which a rational expression is undefined.

Step-by-Step Solution

Answer

A rational expression is undefined for the values that make its denominator equals zero. To find these, identify the denominator, set it equal to zero, and solve for the variable.

Step 1 Identify the Denominator

In a rational expression, the denominator is the expression underneath the fraction bar. For instance, in the expression \(\frac{a}{b}\), 'b' is the denominator. Make it clear.

Step 2 Set the Denominator Equal to Zero and Solve

To find the numbers for which the rational expression is undefined, it's necessary to set the denominator of the expression equal to zero and then solve for the variable. For example, if your denominator is \(b = a + 2\), you would set up the equation \(a + 2 = 0\) and subsequently solve for 'a'.

Step 3 Identify the Numbers for Which the Expression is Undefined

The solution(s) to the equation from Step 2 represent the number(s) that make the denominator of the rational expression equal to zero. These are the numbers for which the rational expression is undefined.