Chapter 14 RATIONAL EXPRESSIONS AND EQUATIONS

Transcription

1 Name: Instructor: Date: Section: Chapter 4 RATIONAL EXPRESSIONS AND EQUATIONS 4 Multiplying and Simplifying Rational Epressions Learning Objectives A Find all numbers for which a rational epression is not defined B Multiply a rational epression by, using an epression such as A/A C Simplify rational epressions by factoring the numerator and the denominator and removing factors of D Multiply rational epressions and simplify Key Terms Use the vocabulary terms listed below to complete each statement in Eercises 4 equivalent multiply rational simplify A quotient, or ratio, of polynomials is a(n) epression Epressions that have the same value for all allowable replacements are called epressions To rational epressions, multiply numerators and multiply denominators 4 To rational epressions, factor the numerator and the denominator and remove a factor of GUIDED EXAMPLES AND PRACTICE Objective A Find all numbers for which a rational epression is not defined Review this eample for Objective A: Find all numbers for which the rational epression 5 is not defined 6 We set the denominator equal to 0 and solve 60 0 Factoring 0 or 0 Using the principle or of zero products Practice this eercise: Find all numbers for which the rational epression n n n 6 is not defined Copyright 0 Pearson Education, Inc Publishing as Addison-Wesley 9

2 Objective B Multiply a rational epression by, using an epression such as A/A Review this eample for Objective B: Multiply: Practice this eercise: Multiply: 8 7y Objective C Simplify rational epressions by factoring the numerator and the denominator and removing factors of Review this eample for Objective C: Simplify: Factoring the comon factor Factoring the numerator 5 and denominator 5 Factoring the 5 rational epression 5 5 Removing a factor of Objective D Multiply rational epressions and simplify Review this eample for Objective D: 4 Multiply and simplify: Multiplying numerators and denominators 5 Factoring numerators 5 and denominators 5 Removing 5 factor of Practice this eercise: Simplify: c c6 c 6 Practice this eercise: 4 Multiply and simplify: t 5 t t t t 7t 0 0 Copyright 0 Pearson Education, Inc Publishing as Addison-Wesley

3 Name: Instructor: Date: Section: ADDITIONAL EXERCISES Objective A Find all numbers for which a rational epression is not defined For etra help, see Eample on page 04 of your tet and the Section 4 lecture video Find all numbers for which a rational epression is not defined 5 7 4a 5 4 p 7 0 Objective B Multiply a rational epression by, using an epression such as A/A For etra help, see Eamples 4 on page 05 of your tet and the Section 4 lecture video Multiply Do not simplify Note that in each case you are multiplying by 5 5a 6c 6 4 5a 7d y6 y7 y y7 7 Copyright 0 Pearson Education, Inc Publishing as Addison-Wesley

4 Objective C Simplify rational epressions by factoring the numerator and the denominator and removing factors of For etra help, see Eamples 5 0 on pages of your tet and the Section 4 lecture video Simplify 8 0ab 4 ab a a a a 00 0 Objective D Multiply rational epressions and simplify For etra help, see Eamples on page 09 of your tet and the Section 4 lecture video Multiply and simplify 4a b b 0a y 7 8y64 y 8 6y6 Copyright 0 Pearson Education, Inc Publishing as Addison-Wesley

5 Name: Instructor: Date: Section: Chapter 4 RATIONAL EXPRESSIONS AND EQUATIONS 4 Division and Reciprocals Learning Objectives A Find the reciprocal of a rational epression B Divide rational epressions and simplify Key Terms Use the vocabulary terms listed below to complete each statement in Eercises interchange multiply To find the reciprocal of a rational epression, the numerator and the denominator To divide by a rational epression, by its reciprocal GUIDED EXAMPLES AND PRACTICE Objective A Find the reciprocal of a rational epression Review this eample for Objective A: Find the reciprocal of each epression a) b) y c) 5 z 6 Practice this eercise: Find the reciprocal of y a a) The reciprocal of is 5 5 b) The reciprocal of y is y c) The reciprocal of z 6 is z 6, or z 6 Copyright 0 Pearson Education, Inc Publishing as Addison-Wesley

6 Objective B Divide rational epressions and simplify Review this eample for Objective B: Divide and simplify: a a a a a 5a6 a a a a a a a 5a6 a a a a a a Multiplying by a 5a6 a a the reciprocal a aa a a 5a6a a aaaa Factoring the a a a a numerator and denominator a a a a Removing a a a aa factor of a a Practice this eercise: Divide and simplify: ADDITIONAL EXERCISES Objective A Find the reciprocal of a rational epression For etra help, see Eamples on page 044 of your tet and the Section 4 lecture video Find the reciprocal y n Objective B Divide rational epressions and simplify For etra help, see Eamples 4 9 on pages of your tet and the Section 4 lecture video Divide and simplify r 9r r r 7r r4 7 y 4 y9 6y y 6y 4 4 Copyright 0 Pearson Education, Inc Publishing as Addison-Wesley