Problem 88 - Algebra and Trigonometry

Question

Explain how to simplify a rational expression.

Step-by-Step Solution

Answer

To simplify a rational expression, one must factor the numerator and the denominator and cancel out common factors.

Step 1: Identify the Expression

Identify the rational expression which is to be simplified. A rational expression is similar to a fraction, but it can have polynomials in the numerator, denominator or both.

Step 2: Factor the Numerator and Denominator

Factor both the numerator and the denominator of the rational expression, breaking them down to their simplest form. This requires knowledge of how to factor various types of polynomials.

Step 3: Cancel Common Factors

After factoring the numerator and the denominator, cancel out the similar factors that appear in both the numerator and the denominator. This step will reduce the expression to its simplest terms.

Step 4: Write the Simplified Expression

Write down the simplified form of the rational expression, keeping in mind that it should already be in its simplest form. If a factor is still common in both the numerator and the denominator, repeat Step 3 to further simplify.