Rational Expressions and Equations

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Rational Expressions and Equations Chapter 6 Rational Expressions and Equations

Chapter Sections 6.1 – The Domains of Rational Functions and Multiplication and Division of Rational Expressions 6.2 – Addition and Subtraction of Rational Expressions 6.3 – Complex Fractions 6.4 – Solving Rational Equations 6.5 – Rational Equations: Applications and Problem Solving 6.6 – Variation Chapter 1 Outline

§ 6.3 Complex Fractions

Simplifying Complex Fractions A complex fraction is one that has a rational expression in its numerator or its denominator or in both the numerator and denominator. Examples of Complex Fractions

Simplify a Complex Fraction by Multiplying by the LCD To Simplify a Complex Fraction by Multiplying by the LCD Find the least common denominator of all fractions appearing within the complex fraction. This is the LCD of the complex fraction. Multiply both the numerator and denominator of the complex fraction by the LCD of the complex fraction found in step 1. Simplify when possible.

Simplify a Complex Fraction by Multiplying by the LCD The LCD is 5x2. Multiply the numerator and denominator by 5x2.

Simplify Complex Fractions by Simplifying the Numerator and Denominator To Simplify a Complex Fraction by Simplifying the Numerator and Denominator Add or subtract as necessary to get one rational expression in the numerator. Add or subtract as necessary to get one rational expression in the denominator. Multiply the numerator of the complex fraction by the reciprocal of the denominator. Simplify when possible.

Example Simplify .