In this lesson from OpenStax Intermediate Algebra 2E, students learn to simplify complex rational expressions — rational expressions that contain other rational expressions in their numerator or denominator. The lesson covers two methods: rewriting the complex expression as division and multiplying by the reciprocal, and using the least common denominator (LCD) to combine and reduce terms. Students practice applying factoring, finding LCDs, and identifying excluded values throughout the simplification process.
Section 1
📘 Simplify Complex Rational Expressions
A complex rational expression is a fraction that contains other fractions in its numerator or denominator. This lesson teaches two powerful methods to simplify them: rewriting as division or clearing fractions using the Least Common Denominator (LCD).
Next, you’ll apply these two methods. We'll start with interactive examples and then move on to practice cards to master each technique.
Section 2
Complex Rational Expression
A complex rational expression is a rational expression in which the numerator and/or the denominator contains a rational expression.
Section 3
Simplify by Writing as Division
To simplify a complex rational expression by writing it as division:
Step 1. Simplify the numerator and denominator so that each is a single rational expression.
Step 2. Rewrite the complex rational expression as a division problem.
Section 4
Simplify Using the LCD
To simplify a complex rational expression by using the LCD:
Step 1. Find the LCD of all fractions in the complex rational expression.
Step 2. Multiply the numerator and denominator by the LCD.
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Section 1
📘 Simplify Complex Rational Expressions
A complex rational expression is a fraction that contains other fractions in its numerator or denominator. This lesson teaches two powerful methods to simplify them: rewriting as division or clearing fractions using the Least Common Denominator (LCD).
Next, you’ll apply these two methods. We'll start with interactive examples and then move on to practice cards to master each technique.
Section 2
Complex Rational Expression
A complex rational expression is a rational expression in which the numerator and/or the denominator contains a rational expression.
Section 3
Simplify by Writing as Division
To simplify a complex rational expression by writing it as division:
Step 1. Simplify the numerator and denominator so that each is a single rational expression.
Step 2. Rewrite the complex rational expression as a division problem.
Section 4
Simplify Using the LCD
To simplify a complex rational expression by using the LCD:
Step 1. Find the LCD of all fractions in the complex rational expression.
Step 2. Multiply the numerator and denominator by the LCD.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter