Answer Key 225

1. 
   

18

54

342

32

xy^3 z

xz^3

= ⋅

⋅

18

18 3

32 4

32

xz^3 y

xz^3

=

⋅

⋅

1818

1818 3

3232 4

3232

xzx^3 y

xzx^3

=y

4

3

2.^15
3

y

y

=

35 ⋅

31 ⋅

y

y

=^5

1

= 5

3. x
   x

−

−

5

5

=

1

1

()x 5

− 1 ()x 5

=

1

1

()()xx^55

− (^1) ()()xx 55

1
− 1
= − 1

4.^4
4

a

+a

is simplifi ed.

5.^26

(^256)
x
xx^2555

(^2) ()x 3
()x^22 ()x^3

(^2) ()()xx 33
()x^22 ()()xx^33
= 2
x− 2
6.
x
xx
2
2
4
44
−

• 
  

  4 xx
  = ()
  x+ ()x
  ()x+ ()x
  )(x−
  )(x+

  
  

  ()()xx+ ()x
  ()()xx+ ()x
  )(x−
  )(x+
  = x
  x
  −

  
  


• 
  

  2
  2

  
  

7. x y
   xy
   ()a+b y()aba

• 
  

  =
  ()ab()xy+
  ()xy+

  
  

  ()ab()()xyxy+
  ()()xyxy+
  = ab
  1
  = a + b

  
  

8. 
   

   7
   35 14
   x
   x−
   = 7
   7
   ⋅
   ()^5 −^2
   x

   
   

   77
   77
   ⋅
   () 5 − 2
   x
   = x
   52 xx
   Chapter 13 Rational Expressions
   Exercise 13