Cogito
Algebra 2 · Chapter 4 · Lesson 2
Adding and Simplifying Rational Expressions
Common denominators, with letters.
11 problems · about 23 minutes · A-APR.D.7
What this lesson teaches
The student simplifies, multiplies, and adds rational expressions.
- Factor before cancelling — only factors may be cancelled.
- Terms that merely look alike cannot be removed.
- Cancelling changes the expression, never the excluded values.
Warm Up
Straightforward practice. Get the method working first.
4 problems(x² − 36)/(x − 6) simplifies to x + what?
Answer 6
Why x + 6.
(x² − 25)/(x − 5) simplifies to x + what?
Answer 5
Why Difference of squares.
Can the x values in (x + 2)/(x + 7) cancel? 1 for yes, 0 for no.
Answer 0
Why They are terms.
(x² − 1)/(x + 1) simplifies to x − what?
Answer 1
Why Factor first.
Build It Up
The same ideas with more to keep track of.
3 problems1/x + 1/x. What is the numerator over x?
Answer 2
Why Same denominator already.
For 5/(x − 6), which x is excluded?
Answer 6
Why Zero denominator.
(3/x) × (x/4). Result as a decimal?
Answer 0.75
Why The x values cancel.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsOrder the steps for simplifying a rational expression.
Answer 1. Factor the numerator and denominator 2. Note the excluded values 3. Cancel shared factors
Why Record what is excluded before cancelling hides it.
Does cancelling restore the excluded value? 1 for yes, 0 for no.
Answer 0
Why The domain never changes.
Simplifying: (x² − 4)/(x − 2) simplifies to x + what?
Answer 2
Why x + 2.
The Excluded Value: For that expression, which x is excluded?
Answer 2
Why x = 2.