Name———————————————————————— Lesson
Lesson 5.4
5.4
Date —————————————
Practice B
For use with the lesson “Multiply and Divide Rational Expressions”
Simplify the rational expression, if possible.
(x 1 7)(x 1 9)
2.​ }}
   ​
(x 2 9)(x 1 7)
3x 2 3
1.​ }
   
​ 
6
x12
x 2 4x 1 4
x 2 1 4x 2 5
4.​ }
   
​ 
x 2 2 25
x 2 1 4x
x 2 2x 2 24
x 2 1 10x 2 11
6.​ }}
    ​ 
x 2 1 7x 2 8
3.​ }
   ​ 
2
5.​ }
  ​ 
2
Multiply the expressions. Simplify the result.
6x 3y 3x 2y
7.​ }
  
​p }
​  3  
​
8x
xy 2
44x7y 4 12xy 5
8.​ }
  
​ p }
​  5 3 
 ​ 
22x y
5xy 2
5x(x 2 2)
(x 1 1)(x 2 6)
(x 1 1)
10(x 2 2)(x 2 1)
9.​ }}
  
 
 ​p }}
​ 
  
   ​
x 2 2 9x 1 20
x 1 9x 1 14
x 2 1 6x 1 8
x 2 x 2 20
11.​ }
  
​p }
​  2
  
​
2
x 2 1 4x 1 3 x 2 2 3x 2 10
10.​ }
  
​p }
​ 
   
​ 
x2 1 x
x 2 1 5x 1 6
x 3 1 3x 2
x 3 2 9x
12.​ }
  ​ 
p}
​  x 2 3   
​ 
2
x 1 6x 1 9
Divide the expressions. Simplify the result.
2x 2 1 4x
x 24
24x 2y
16x 2y
14.​ }2  
​4 }
​  3 3 
 ​ 
54x y
81xy
x 2 2 3x 1 2
15.​ }
  
​ 
4}
​  3x 2 6   
​ 
2
x 2 2 3x 2 18
x 2 9x 1 18
17. (x 2 1 9x 1 18) 4 }
​  2
  
​
3x 2 2 12x
9x 2
}
16.​ }
  ​ 
4
​ 
  
​ 
6x 2 3
2x 2 2 x
x11
3x 2 1 4x 1 1
18.​ }
   
​ 
4 ​ }
   ​ 
2
2
x
1
8x 1 12
x 24
19. Geometry In the diagrams below, the length of the edge of the square is twice as
long as the radius of the circle. Find the ratio of the area of the circle to the area of
the square. Write your answer in simplified form.
r
x
x
5-42
Algebra 2
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
6x 2y
10x 4
13.​ }2  
​4 }
​  4  
​
xy
3xy
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