Problem 95 - Introductory Algebra for College Students

Question

Explain how to simplify a rational expression.

Step-by-Step Solution

Answer

A rational expression can be simplified by factorizing the numerator and denominator and then cancelling out any common factors. The simplified form is the result when no common factors exist in the numerator and the denominator.

Step 1: Identify the Rational Expression

First identify the rational expression that needs to be simplified. A rational expression, or algebraic fraction, in most general form can be written as \(\frac{P(x)}{Q(x)}\), where \(P(x)\) and \(Q(x)\) are polynomials.

Step 2: Factor the Numerator and the Denominator

Factorize the polynomials in the numerator and the denominator. The process may involve pulling out common factors, grouping, or using a special factoring formula depending on the given polynomials.

Step 3: Cancel Common Factors

Upon successful factorization, look for any common factors that appear in both the numerator and the denominator. Cancel these out to simplify the expression. Remember, this can only be done if the common factor is multiplied by the entire numerator and the entire denominator.

Step 4: Write the Simplified Expression

After cancelling out the common factors, rewrite the expression. This will be the simplified form of the rational expression.