Problem 91 - College Algebra Essentials

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, simply add or subtract the numerators and place the result over the common denominator. Then simplify if possible.

Step 1: Visualize the Rational Expressions

Think of the rational expressions as fractions. For example, let the expressions be \(a/b\) and \(c/b\), where a, b, and c are polynomials and b is the common denominator.

Step 2: Perform the Operation

Add or subtract the numerators while keeping the denominator the same. If we were adding the two expressions, we would get \((a+c)/b\). If we were subtracting, the result would be \((a-c)/b\).

Step 3: Simplify if Possible

Look at the new numerator created (whether it's \(a+c\) or \(a-c\)) and see if it can be simplified further. Sometimes, this might involve factoring the numerator and cancelling common terms with the denominator.