Name———————————————————————— Lesson

5.4

Date —————————————

Practice A

For use with the lesson “Multiply and Divide Rational Expressions”

Lesson 5.4

Simplify the rational expression, if possible. (x 2 3)(x 1 1) 2. ​ }}    ​ (x 2 2)(x 2 3)

3x 1. ​ }    ​   3x 2 6 x12 4(x 2 3)

x2 2 9 4. ​ }   ​  2 x 1 5x 1 6

x 2 1 5x 1 4 x 2 16

x 2 2 2x 2 8 6. ​ }    ​  x 2 1 7x 1 10

3. ​ }   ​   5. ​ }     ​   2

Multiply the expressions. Simplify the result. 18x 2y 3 14xy 8. ​ }    ​ p } ​  4   ​ 12x 7xy 2

27xy 4x 2 7. ​ }    ​ p } ​  3  ​   8x 3xy x26 x(x 2 1)

x 2 2 1 (x 1 2)(x 2 1) 10. ​ }   ​p }} ​  x 2 1     ​  x11

x2 2 x 2 2 x 1 4x 1 3

x 2 2 4 x 2 2 5x 2 6 12. ​ }   ​p } ​     ​ 2x 1 2 x 2 2 6x 1 8

3x (x 1 3)(x 2 6)

9. ​ }}      ​p } ​    ​   x 2 1 3x x 2 3x 1 2

11. ​ }   ​  p} ​  2    ​   2 Divide the expressions. Simplify the result.

8xy 2 32x 4y } 14. ​ }     ​ 4 ​     ​ 21y 4 3xy 2

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.

3xy 12y 3 13. ​ }    ​4 } ​  3  2 ​   2 4x y 5x y 4x 2 x 1x26

x15 x 2 1 x 2 20 16. ​ }    ​4 } ​ x 2 3   ​ 2 x 2 x 2 12

2x

15. ​ }    ​  4} ​ x 1  3 ​   2 x 2 2 5x 1 6 x 2 8x 1 12

x 2 1 x 2 12 x 2 6x

17. ​ }    ​  4} ​  2     ​   2

x 2 1 8x 1 16 2x 2 1 7x 2 4 } 18. ​ }     ​ 4 ​     ​ x 2 1 x 2 12 x 2 2 6x 1 9

19. Storage Crates  A cranberry farmer has two different styles of storage crates to

transport the produce from the farm to the processing facility. The first crate style is larger than the second because it is intended for use with mass transit. Use the diagrams below to find the ratio of the volume of the larger crate to the volume of the smaller crate.



3x 1 6



x 2x x16 Small crate

2x 1 12 4x Large crate

Algebra 2 Chapter Resource Book

5-41

answers

Lesson 5.4 Multiply and Divide Rational Expressions, continued Practice Level A x23 x x11 1. ​ }    ​  2. } ​ x 2 2   ​ 3. not possible 4. } ​ x 1 2   ​ x22 3y 2 9x x11 x24 5. } ​ x 2 4   ​ 6. } ​ x 1 5   ​ 7. } ​  2  ​  8. ​ }   ​ 2y x2 3 x 9. ​ }}     ​ 10. (x 1 2)(x 2 1) 11. } ​ x 2 1 ​  (x 1 3)(x 2 1) (x 1 2)(x 2 6) 16y 3 12. }} ​       ​  13. ​ }     ​  14. 28x 2y 5 2(x 2 4) x23 2x x22 x13 12(x 1 2) 19. } ​  x      ​

x x14

2. about 11% 3. 5, 6, and 7 4. about 320 members, about 37 trumpet players 5. about 11.4%

Challenge Practice (4x 1 1)(5x 1 6)(x 1 2) 5(t 1 5) 1. 2​ }}       ​ 2. } ​  3    ​  (4x 1 5)(x 1 1)(x 2 6) 4t

(x n 2 8)(x n 2 5) x4     ​  3. } ​  n   2 ​ 4. }} ​  n n (x 1 1) x (x 1 1) 5. horizontal asymptote: y 5 1;

y

vertical asymptote: x 5 21 2

2x 2 1 x23

15. } ​     ​  16. } ​     ​ 17. } ​     ​ 18. ​ }   ​

6. horizontal asymptote: y 5 0;

y

vertical asymptote: x 5 3 2

7. horizontal asymptote: y 5 0;

Study Guide 1. The ratio of surface area to volume is greater for the old can, so the old can is less efficient than the new can.

3(x – 6) 2x x14 1 2. } ​ 3y ​ 3. } ​ 3 ​ 4. } ​ x 2 2   ​ 5. } ​  4    ​ 

Real-Life Application 2953.05y 2 1 22,360.5y 1 55,000 1. P 5 }}} ​          ​ 22355.64y 2 1 120,167.27y 1 638,700

A8

Algebra 2 Chapter Resource Book

y

}

vertical asymptotes: x 5 6​Ï 5 ​ 

1 x

2

Practice Level C 8. horizontal asymptote: y 5 0; x17 x 2 1 3x 1 9 1. } ​  2x    ​  2. not possible 3. } ​  x 1 3    ​  vertical asymptotes: x 5 61 15y 55x7 y 4 (x 1 5)(x 2 4) 4. } ​ 4x  ​ 5. ​ }    ​  6. 2x 7. }} ​       ​  3x(x 1 7) 32z 3 2(2x 1 3) (2x 1 5)(x 2 4) x 8. } ​  2    ​  9. 1 10. }} ​       ​  11. } ​ x 1 1 ​  3(x 1 2) x (x 1 2) x(x 2 6) (x 1 2)(x 1 6) x2 1 1 1 21 12. } ​     ​ 13. }} ​       ​ 14. }} ​       ​   9. }} ​  }  }   ​ 10. }} ​  }   }   ​ 2x 4x(x 1 2) (2x 2 1)(x 2 2) ​Ï x 1 h ​  1Ï ​ x ​  ​Ï x 2 h ​  1Ï ​ x ​  2x  π r  π   15. } ​ x 1  1 ​  16. } ​  2   ​ 17. } ​ 8  ​ 18. about 6594 gal 1 11. ​ }}    }  } ​ ​Ï x 1 h 1 1 ​  1Ï ​ x 1 1 ​  19. 30 ft by 15 ft by 5 ft

x

2

y

1 2

x

1 12. ​ }}    }  } ​ Ï ​ x 1 h 2 2 ​  1Ï ​ x 2 2 ​ 

Lesson 5.5 Add and Subtract Rational Expressions Teaching Guide 1. 40; Sample answer: There are no common 25 49 24 factors, so the LCD is 8 p 5, or 40. ​ }  ​ 1 } ​ 40 ​ 5 } ​ 40 ​  40

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Practice Level B x19 x21 x21 1. } ​  2    ​  2. } ​ x2 9   ​ 3. not possible 4. } ​ x 2 5   ​ 24x 2 y 4 9x x x 1 11 5. ​ }    ​  6. } ​     ​ 7. } ​    ​ 8. } ​      ​  5 x26 x18 4 x25 x x24 9. ​ }}     ​ 10. } ​  x       ​ 11. } ​ x 1 7   ​ 12. x 3 2(x 2 6)(x 2 1) 5x 2 y 4x 2 y 6x x2 13. } ​  9    ​  14. ​ }      15. ​ }} ​      ​ 16. } ​     ​  9 x24 (x 2 2)(x 2 1) (3x 1 1)(x 1 6)  π  17. (x 1 6)(x 2 3) 18. }} ​       ​  19. ​ }  ​ x22 4

x

1