1. Adding and Subtracting Rational Expressions
ALGEBRA 1 LESSON 12-6
pages 669–671  Exercises 1. 2. 3. 4. 5. 6. 7.
8. – 9. 9 2m 7
6t – 1
n + 2
n + 3 14
c – 5
2s2 + 1
4s2 + 2
6c – 28
2c + 7 –3
2 – b 1
t 2 + 1
–2t
2t – 3
10. 1
11. 2
12. –1
13. 2x2
14. 18
15. 7z
16. 35b3c
17.
18.
19.
20.
35 + 6a
15a
12 – 2x 3x x2
15x8
9 + 2m
24m3
21.
22.
23.
24.
25.
26.
27.
28.
29. a b.
c. about 0.8 h
189 – 9n
7n3 x2
20x2
17m – 47
(m + 2)(m – 7)
a2 + 9a + 12
(a + 3)(a + 5)
a2 + 12a + 15
4(a + 3)
c2 + 7c + 20
(c + 5)(c + 3)
4t 2 + 5t + 5
t 2(t + 1)
18a + 3
(2a + 1)(2a – 1) r
0.7r 17 7r
12-6

2. Adding and Subtracting Rational Expressions
ALGEBRA 1 LESSON 12-6
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
–y 2 + 2y + 2
3y + 1
h 2 + h + 1
2t 2 – 7
r – 2k – 6
9 + p3
–3 – x – z
xy 2z
k + 3km
2m2
12c – 15a
abc
c 3 – a3
10x + 15
x + 2
–21t + 33
2t – 3 6x
(x – 3)(x + 3)2
40.
41. The student added the
terms in the denominators.
42. a ;
b ;
c. Yes; they both represent
the time it takes to make
a round trip.
43. Answers may vary. Sample:
Not always; the numerator
may contain a factor of the LCD.
44. Answers may vary.
Sample: , ;
k – 1
k – 6 2 r
1.25r 18 5r d
0.8d 9 2d 2w
w + 3
3w 2
w – 3
3w3 + 11w2 – 6w
(w + 3)(w – 3)
45.
46. 8
47.
48.
49.
50.
51. –
52.
53.
54.
55. D
8x 2 – 1 x
– 3x – 5
x(x – 5)
32x
x – 5 4x 1
2x(x – 5)
d + 3
d + 4
–x3 + 6x2 + 35x – 50
(a + 12)(a – 5)
x + 4
5a – 8
(a + 2)(a – 5)
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3. Adding and Subtracting Rational Expressions
ALGEBRA 1 LESSON 12-6
56. H
57. D
58. [2] a = total time;
= = =
b = =
= =
The ride took 1 hours.
[1] one computational error
OR no work shown 10 r
r + 3
10(r + 3) + 10r
r(r + 3)
10r r
20r + 30
10(2r + 3)
10(2(12) + 3)
12(12 + 3)
10(24 + 3)
12(15)
10(27)
180
270 3 2
x – 1
60. 5b2 – 10b + 30 –
61. 6
62. 3
63. no solution
64. ± 6.9
65. ± 3.9
66. no solution x2 60
b + 2 1
12-6