Factor the top and bottom first. Nothing can be cancelled until it is a factor.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The commonest error
In (x + 3)/(x + 5) the x values cannot cancel. They are terms, not factors.
Multiplying
Multiply straight across, then cancel shared factors.
Adding
A common denominator is required first, exactly as with numbers.
Common denominators, with letters
Adding rational expressions works exactly like adding fractions: factor each denominator, build the least common denominator, rewrite both, then add numerators. The letters change nothing about the method.
Factor before anything else
Factoring both denominators reveals the common factors and the least common denominator. Multiplying the denominators together always works but produces expressions far larger than necessary.
The numerator needs brackets
When subtracting, the whole numerator is subtracted, so bracket it before distributing the minus. Dropping those brackets and subtracting only the first term is the standard error in the topic.
Cancel factors, never terms
You may cancel a factor common to the whole numerator and the whole denominator. You may not cancel a term from a sum: (x + 3)/(x + 5) does not reduce. This is the most persistent misconception in all of algebra.
Step 2: Try It Yourself
Tap and try it out.
Step 3: Watch an Example
One step at a time.
Watch Naomi Cancel Correctly
Naomi simplifies (x² − 9) / (x + 3).
- Step 1
She factors the numerator: (x − 3)(x + 3).
Step 4: Your Turn
Practice makes it stick.
Simplifying
Problem 1 of 2
(x² − 4)/(x − 2) simplifies to x + what?
The Excluded Value
Problem 2 of 2
For that expression, which x is excluded?
Factor, Then Cancel
1 of 8
(x² − 25)/(x − 5) simplifies to x + what?
2 of 8
Can the x values in (x + 2)/(x + 7) cancel? 1 for yes, 0 for no.
3 of 8
(x² − 1)/(x + 1) simplifies to x − what?
4 of 8
1/x + 1/x. What is the numerator over x?
5 of 8
For 5/(x − 6), which x is excluded?
6 of 8
(3/x) × (x/4). Result as a decimal?
7 of 8
Order the steps for simplifying a rational expression.
- 1Note the excluded values
- 2Cancel shared factors
- 3Factor the numerator and denominator
8 of 8
Does cancelling restore the excluded value? 1 for yes, 0 for no.
Step 5: Quick Check
Show what you know.
Question 1 of 1
(x² − 36)/(x − 6) simplifies to x + what?
What You Learned
- Factor before cancelling — only factors may be cancelled.
- Terms that merely look alike cannot be removed.
- Cancelling changes the expression, never the excluded values.