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Course: Algebra II / Intermediate Algebra
Topic: Rational Expressions
Subtopic: Operations IV - Add & Subtract (different denominators)

Overview

In this lesson we add and subtract rational expressions that have different denominators. This is more complicated than when the denominators match.

Recall that adding numeric fractions that have different denominators such as 5/6 + 2/15 requires finding an LCD, building each fraction up to have that LCD, adding the fractions, and simplifying the answer. Similarly for rational expressions we must do all these steps except that the numerators and denominators will be algebraic expressions and the LCD is likely to be a factored polynomial.

To add/subtract rational expressions that have different denominators:

- Factor each denominator completely.
- Find the LCD. Watch for opposites!
- Build each fraction up to have the LCD by multiplying each
fraction by an expression equivalent to 1 (e.g. (x-3)/(x-3)).
- Combine into a single fraction. (If subtracting distribute the
minus sign throughout the numerator. Watch the signs!)
- Simplify the numerator completely.
- Reduce the fraction by factoring and canceling if possible.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 8.4.1 Add or subtract rational expressions that have different denominators using their LCD as needed
• 8.4.2 Deal with opposites when finding the LCD of rational expressions being added or subtracted

Terminology

Define: LCD = lowest common denominator, "build up" a fraction to have a given denominator

Supplemental Resources

Read my Lecture - Application of Rational Functions for motivation.