Problem 91 - Algebra and Trigonometry

Question

Explain how to add or subtract rational expressions with the same denominators.

Step-by-Step Solution

Answer

To add or subtract rational expressions with the same denominator, keep the denominator and add or subtract the numerators directly. Then, if possible, simplify the resulting rational expression.

Step 1: Write down the rational expressions

Let's take two general rational expressions with the same denominators, \(\frac{A}{C}\) and \(\frac{B}{C}\), where A, B, and C are polynomials.

Step 2: Add/Subtract the rational expressions

To add or subtract these expressions, keep the denominator the same, and directly add or subtract the numerators. This means that \(\frac{A}{C} + \frac{B}{C} = \frac{A+B}{C}\) and \(\frac{A}{C} - \frac{B}{C} = \frac{A-B}{C}\).

Step 3: Simplification

After performing the operation, simplify the resulting rational expression if possible. This could involve factoring the numerator and canceling common factors with the denominator.