Problem 96 - Introductory Algebra for College Students

Question

Explain how to simplify a rational expression with opposite factors in the numerator and denominator.

Step-by-Step Solution

Answer

To simplify a rational expression with opposite factors in the numerator and denominator, identify any shared factors between the top and bottom of the fraction, and 'cancel' them out to simplify the ratio. The result is your simplified rational expression.

Step 1: Identify Common Factors

Firstly, it is important to identify any common factors that appear both in the numerator and the denominator of the rational expression.

Step 2: Rule of Division

According to the rules of algebra, any factor divided by itself equals 1. Therefore, when the same factor appears in both the numerator and the denominator of a fraction, they can be 'cancelled out' or divided by each other to simplify the ratio.

Step 3: Simplify the Expression

After identifying and cancelling all the common factors, the remaining terms in the numerator and denominator simplify the expression. There might be a need to further simplify the resulting expression by gathering like terms or using other arithmetic properties, but that's determined by the given expression.