Lesson 3.6

Adding & Subtracting (Like Denominators)

When the denominators are already the same, adding or subtracting rational expressions is as simple as combining the numerators.

Introduction

Just as , when two rational expressions share the same denominator, you simply add (or subtract) the numerators and keep the denominator.

Past Knowledge

Adding fractions with like denominators and combining like terms.

Today's Goal

Combine numerators over the common denominator, then simplify the result.

Future Success

This is the easy case. Lesson 3.7 handles unlike denominators using the LCD from Lesson 3.5.

Key Concepts

The Rules

Don't Forget!

After combining, always:

1

Distribute the minus sign (if subtracting)

2

Combine like terms in the numerator

3

Factor and simplify if possible

Worked Examples

Example 1: Simple Addition

Basic

Add .

1

Combine numerators

Example 2: Subtraction with Distribution

Intermediate

Subtract .

1

Combine numerators

2

Factor & cancel

Example 3: Multi-Term Subtraction

Advanced

Subtract .

1

Combine and distribute the minus

2

Factor denominator

Common Pitfalls

Forgetting to Distribute the Negative

, not . Use parentheses!

Skipping the Simplify Step

After combining, always check if the result can be factored and simplified further.

Real-Life Applications

In economics, combining cost and revenue functions often involves adding rational expressions with common denominators. The ability to simplify the result reveals break-even points and profit margins.

Practice Quiz

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