Problem 93 - Introductory Algebra for College Students

Question

What is a rational expression? Give an example with your explanation.

Step-by-Step Solution

Answer

A rational expression is an expression of the form \( \frac{P(x)}{Q(x)} \), where \( P(x) \) and \( Q(x) \) are polynomials and \( Q(x) \) ≠ 0. An example of a rational expression is \( \frac{x^2}{x+1} \).

Step 1: Define Rational Expression

A rational expression is an expression of the form \( \frac{P(x)}{Q(x)} \), where \( P(x) \) and \( Q(x) \) are polynomials, and \( Q(x) \) is not 0.

Step 2: Identify Parts of a Rational Expression

In any rational expression, the \( P(x) \) is referred to as the numerator, while \( Q(x) \) is the denominator. The denominator \( Q(x) \) cannot be equal to 0 because division by 0 is undefined in mathematics.

Step 3: Give an Example of a Rational Expression

An example of a rational expression can be \( \frac{x^2}{x+1} \). Here, \( x^2 \) is the numerator and \( x+1 \) is the denominator. This expression is valid for all values of \( x \) except when \( x \) is equal to -1 since it would make the denominator zero and the expression would be undefined.