College Algebra 9th txtbk

38 CHAPTER R BASIC ALGEBRAIC OPERATIONS
x 2 9x 20 3x 2 y 3
2a 2 b 4 c 6
8. 9. 10.
x 2 16
x 4 y
6a 5 b 3 c
In Problems 11–36, perform the indicated operations and reduce
answers to lowest terms. Represent any compound fractions as
simple fractions reduced to lowest terms.
5
11.
6 11
15
12.
1
13.
8 1 9
14.
1
m
15. 16.
n n n 1 m
m
5
17. 18.
12 3 4
19. a25 20.
8 5
16 b 4
15
b 2
21. a b2
22.
2a a b a a
2a b a 2b a
3b
2 3b b
x 2 1
x 2 9
23. 24.
x 2 1 x 3
x 2 x 1
x 2 4
x 1
1
1
25. 26.
bc 1 ac 1
c 1 b 1 a
ab
2a b
27.
a 2 b 2a 3b
2 a 2 2ab b 2
28.
29. m 2 m 2
x 1
30.
m 1
x 1 x
3
1
31. 32.
a 3 2
x 2 2
2 x
3 a
33.
34.
x 2
x 2 1 x 2
(x 1) 2
3
y 2 2
y 2
4x
x 2 y 2 3
x y 2
x y
x 2
4
y 1
x x
2
35. 36.
x
2
y 1
x 1
Problems 37–42 are calculus-related. Reduce each fraction to
lowest terms.
6x 3 (x 2 2) 2 2x(x 2 2) 3
37.
x 4
4x 4 (x 2 3) 3x 2 (x 2 3) 2
38.
x 6
4y
y 2 4
2x(1 3x) 3 9x 2 (1 3x) 2
39.
(1 3x) 6
40. 2x(2x 3)4 8x 2 (2x 3) 3
(2x 3) 8
7
10 19
25
9
8 8 9
10
3 5 2
25
8 a 5
16 4
15 b
2x(x 4) 3 3(3 x 2 )(x 4) 2
41.
(x 4) 6
3x 2 (x 1) 3 3(x 3 4)(x 1) 2
42.
(x 1) 6
In Problems 43–54, perform the indicated operations and reduce
answers to lowest terms. Represent any compound fractions as
simple fractions reduced to lowest terms.
43.
44.
45.
46.
47.
48.
49.
50.
y
y 2 2y 8 2
y 2 5y 4 1
y 2 y 2
x
x 2 9x 18 x 8
x 6 x 4
x 3
16 m 2
m 2 3m 4 m 1
m 4
x 1
x(1 x) x2 2x 1
x 2 1
x 7
ax bx y 9
by ay
c 2
5c 5 c 2
3c 3 c
1 c
x 2 16
2x 2 10x 8 x2 13x 36
x 3 1
a x3 y 3
y 3
y
x y b x2 xy y 2
y 2
x
51. a
x 2 16 1
x 4 b 4
x 4
3
52. a
x 2 1
x 1 b x 4
x 2
x
1 2 y 2 y x 15
x 2
x
53. 54.
x
1 4 y y x 5 x 2
x
Problems 55–58 are calculus-related. Perform the indicated
operations and reduce answers to lowest terms. Represent any
compound fractions as simple fractions reduced to lowest terms.
1
1
(x h) 1 x h 1 x
2 x 2
55. 56.
h
h
(x h) 2
2x 2h 3
x h 2
x2
x 2
x h
57. 58.
h
h
s 2
y
y2
y x
s t s
59. 60.
t 2
1 x2
y s t t
2 x 2
2x 3
x
In Problems 59–62, perform the indicated operations and reduce
answers to lowest terms. Represent any compound fractions as
simple fractions reduced to lowest terms.