1.4 Rational Expressions
Combine fractions and keep domain restrictions.
Before you solve
Ideas in this lesson
Review the ideas below. Select one to see worked steps and five practice questions.
01Domain of an algebraic expressionWorked steps · five questions02Simplifying rational expressionsWorked steps · five questions03Multiplying and dividing rational expressionsWorked steps · five questions04Adding and subtracting rational expressionsWorked steps · five questions05Compound fractionsWorked steps · five questions06Rationalizing a denominator or numeratorWorked steps · five questions07Avoiding common algebra errorsWorked steps · five questions08Simplify structured quotients and radical combinationsWorked steps · five questions09Interpret and evaluate rational modelsWorked steps · five questions10Investigate excluded inputs and prove boundsWorked steps · five questions
Lesson brief and rules
1.4 Rational Expressions
Use a common denominator before adding or subtracting rational expressions. Factor before canceling common factors.
Remember
Cancel common factors, never individual terms in a sum. Keep all original domain restrictions.
Cancel common factors, never individual terms in a sum. Keep all original domain restrictions.
Worked example
01 / Find the real domain of .
02 / The numerator does not restrict this rational expression.
03 / Factor the denominator: .
04 / Both denominator zeros must be excluded: .
Worked example 2 · Domain of an algebraic expression
Find the real domain of .
A square root allows zero but does not allow a negative radicand.
Require , which is equivalent to .
Including the endpoint gives .
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.