FNDMATH Module 3 Handout - Rational Expressions PDF
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This document provides examples and explanations for simplifying, adding, subtracting, multiplying and dividing rational expressions in mathematics, useful for students in algebra or precalculus level courses.
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Lecture 3 Lecture 3 RATIONAL EXPRESSIONS Simplifying Rational Expression Addition/Subtraction of Rational Expression Multiplication/Division of Rational Expression...
Lecture 3 Lecture 3 RATIONAL EXPRESSIONS Simplifying Rational Expression Addition/Subtraction of Rational Expression Multiplication/Division of Rational Expression Complex Rational Expression 1 2 Rational Expressions A rational expression is a ratio or quotient of two polynomials P( x) Q( x) where P(x) and Q(x) are polynomial The denominators should not be equal to zero (domain restriction) FNDM ATH 1 2 Lecture 3 3 Rational Expressions Exercise 4.1: Determine which of the following is a rational expressions x 2 3x 2 x2 4x 3 ___1. ___ 4. x4 2 1 1 ___2. ___ 5. 3x 2 x2 x2 3x 1 ___3. x3 4 3 4 Simplifying Rational Expressions 1. Factor the numerator and denominator completely. 2. State any domain restriction. 3. Cancel (divide out) the common factors in the numerator and denominator. FNDM ATH 2 4 Lecture 3 5 Adding/Subtracting Rational Expressions 1. Factor each the denominators completely. 2. Determine the LCD (the product of each factors raised to the highest power to which that factor appears in the denominators. 3. Write each rational expressions using the LCD for each denominator. 4. Perform the resulting operation in the numerators. 5. Simplify by removing the common factors. 5 6 Adding/Subtracting Rational Expressions Perform the indicated operation and simplify 5x 7x 2 1) 2 2x 6 x x 6 3x 3 x 2) 2 x 4 x2 1 4 2 3) 2 2 y y 4 y 2y 3 x x 2 4) 3 2x 1 x 1 x 3 4 y2 y 5) 2 5 y 6 y 2 5 y 4 y 12 FNDM ATH 3 6 Lecture 3 7 Adding/Subtracting Rational Expressions Perform the indicated operation and simplify 5x 7x 2 1) 2 2x 6 x x 6 3x 3 x 2) 2 x 4 x2 1 4 2 3) 2 2 y y 4 y 2y 3 x x 2 4) 3 2x 1 x 1 x 3 4 y2 y 5) 2 5 y 6 y 2 5 y 4 y 12 7 8 Adding/Subtracting Rational Expressions Perform the indicated operation and simplify 5x 7x 2 1) 2 2x 6 x x 6 3x 3 x 2) 2 x 4 x2 1 4 2 3) 2 2 y y 4 y 2y 3 x x 2 4) 3 2x 1 x 1 x 3 4 y2 y 5) 5 y 6 y 2 5 y 2 4 y 12 FNDM ATH 4 8 Lecture 3 9 Adding/Subtracting Rational Expressions Perform the indicated operation and simplify 5x 7x 2 1) 2 2x 6 x x 6 3x 3 x 2) 2 x 4 x2 1 4 2 3) 2 2 y y 4 y 2y 3 x x 2 4) 3 2x 1 x 1 x 3 4 y2 y 5) 2 5 y 6 y 2 5 y 4 y 12 9 10 Multiplication of Rational Expressions 1. Factor the numerators and denominators the expressions completely. 2. Write as a single fraction or rational expressions. 3. Simplify by removing the common factors in the numerator with factors in the denominator. 4. Multiply the remaining factors in the numerator and the remaining factors in the denominator. (Sometimes no need to perform) FNDM ATH 5 10 Lecture 3 11 Division of Rational Expressions 1. Factor the numerators and denominators the expressions completely. 2. Get the reciprocal of the divisor. 3. Multiple the dividend with the reciprocal of the divisor. 4. Write as a single fraction or rational expressions. 5. Simplify by removing the common factors in the numerator with factors in the denominator. 6. Multiply the remaining factors in the numerator and the remaining factors in the denominator. (Sometimes no need to perform) 11 12 Multiplication/Division of Rational Expressions Perform the indicated operation and simplify 3 x 2 12 x2 5x 1) 2 x x 3 x 10 y 3 y 10 y 25 2 2) 3 y 9 y 2 3 y 40 20 x 2 3x 2 12 x 2 23 x 5 3) 25 x 2 4 3x 2 5x 2 p 2p 4 4) 2 p 1 p 1 w2 w w3 w 5) w 5w3 FNDM ATH 6 12 Lecture 3 13 Multiplication/Division of Rational Expressions Perform the indicated operation and simplify 3 x 2 12 x2 5x 1) 2 x x 3 x 10 y 3 y 2 10 y 25 2) 3 y 9 y 2 3 y 40 20 x 2 3x 2 12 x 2 23 x 5 3) 25 x 2 4 3x 2 5x 2 p 2p 4 4) 2 p 1 p 1 w2 w w3 w 5) w 5w3 13 14 Simplifying Complex Rational Expressions Simplify 2 x 1) 3 4 x 1 1 3 2) x 2 9 x 1 2x 6 3 3 3) x 1 x 1 5 x 1 2 FNDM ATH 7 14 Lecture 3 15 Simplifying Complex Rational Expressions Simplify 2 x 1) 3 4 x 1 1 3 2) x 2 9 x 1 2x 6 3 3 3) x 1 x 1 5 x 1 2 15 3 x x 2 2 x 4) 3 1) 2x 1 x 1 x 3 4 3 4 y2 y x 1 5) 2 5 y 6 y 2 5 y 4 y 12 2 p 2p 4 4) p2 1 p 1 w2 w w3 w 5) w 5w3 FNDM ATH 8 16
