Simplifying Rational Expressions
Factor and cancel common factors.
Key idea
Factor and cancel common factors.
In depth
Factor top and bottom completely, then cancel common factors, not common terms. Note any values excluded in the original expression.
Worked example
(x² − 9)/(x² + 3x) = (x−3)(x+3)/(x(x+3)) = (x−3)/x, with x ≠ 0, −3.
Real-world uses
- Cancelling terms in engineering formulas to reduce mistakes before substituting numbers
Common mistake
Cancelling terms like x in (x + 2)/x.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Simplifying Rational Expressions?
Factor and cancel common factors. It is a topic at the advanced level in Algebra.
Where is Simplifying Rational Expressions used in real life?
Real-world examples: Cancelling terms in engineering formulas to reduce mistakes before substituting numbers.
What should I learn before Simplifying Rational Expressions?
Make sure you are comfortable with Rational Expressions, the previous topic in Algebra.
What is a common mistake with Simplifying Rational Expressions?
Cancelling terms like x in (x + 2)/x.
How can I practise Simplifying Rational Expressions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Simplifying Rational Expressions?
Move on to Rational Expression Operations next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.