Lesson 3.2
Simplifying Rational Expressions
Simplifying a rational expression works just like simplifying a numeric fraction: factor the top and bottom, then cancel common factors.
Introduction
Just as simplifies to by cancelling a common factor of 2, rational expressions simplify by cancelling common polynomial factors.
Past Knowledge
All factoring techniques from Unit 2 and domain restrictions from Lesson 3.1.
Today's Goal
Factor numerator and denominator, then cancel common factors to simplify.
Future Success
Simplifying is the prerequisite for every other rational operation.
Key Concepts
The Process
Factor the numerator completely
Factor the denominator completely
Cancel any factors that appear in BOTH
State the domain restrictions from the original denominator
Critical Rule
You can only cancel factors (things being multiplied), never terms (things being added/subtracted).
✓ Correct
✗ Wrong
Worked Examples
Example 1: GCF Cancellation
BasicSimplify .
Factor
Cancel
Example 2: Factoring Trinomials
IntermediateSimplify .
Factor top & bottom
Cancel
Example 3: Opposite Factors
AdvancedSimplify .
Factor denominator
Recognize
Common Pitfalls
Cancelling Terms Instead of Factors
. The 5 in the numerator is being added, not multiplied.
Dropping Domain Restrictions
Even after cancelling , the restriction remains.
Real-Life Applications
In physics, simplifying rational expressions is essential for deriving formulas. The lens equation requires combining and simplifying rational expressions to solve for any unknown.
Practice Quiz
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