Rational Expressions
Fractions with polynomials in numerator and denominator.
Key idea
Fractions with polynomials in numerator and denominator.
In depth
A rational expression is a ratio of polynomials. It behaves like a fraction, but it is undefined where the denominator equals zero, so you must state those excluded values.
Worked example
(x + 1)/(x − 3) is undefined at x = 3.
Real-world uses
- Combining average speeds or unit costs in formulas
- Modelling rates in chemistry and physics
Common mistake
Forgetting the restriction after simplifying.
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 Rational Expressions?
Fractions with polynomials in numerator and denominator. It is a topic at the advanced level in Algebra.
Where is Rational Expressions used in real life?
Real-world examples: Combining average speeds or unit costs in formulas; Modelling rates in chemistry and physics.
What should I learn before Rational Expressions?
Make sure you are comfortable with Quadratic Applications, the previous topic in Algebra.
What is a common mistake with Rational Expressions?
Forgetting the restriction after simplifying.
How can I practise 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 Rational Expressions?
Move on to Simplifying Rational Expressions 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.