1. Simplifying Rational Expressions
ALGEBRA 1 LESSON 12-3
pages 654–656  Exercises 1. 2. 3. 4.
5. 3x 6. 7. 8. 9.
2a + 3 4 1 7x 3 2
x + 2 x2
b + 4
m – 7
10.
11.
12.
13.
14. b + 3
15.
16. –1
17.
18. –2
19. – w
w – 7
a + 1 5
m + 3
m + 2
c – 4
c + 3
m – 2 –4
t + 1
20. –
21. –
min
min
min
25.
26.
27.
28.
29.
w – 4
2r – 1
r + 5
v + 5
7z + 2
z – 1
4a2
2a – 1
5t – 4
3t – 1
3(z + 4) z3
12-3

2. Simplifying Rational Expressions
ALGEBRA 1 LESSON 12-3
30.
31. –
32.
33.
34. Answers may vary. Sample:
35. a. i.  ii. 
b. ;
36. The student canceled terms
instead of factors.
37. –3 is not in the domain of
38.
39.
40.
41.
42.
43.
44.
45. sometimes
46. sometimes
47. never
48. C
49. I
50. B
51. D
52. C
53. [2] The student put the
4 in the numerator
rather than in
the denominator. =
[1] no explanation OR
incorrectly simplified
expression
2s + 1 s2 5w
5w + 6
2a + 1
a + 3 1 4 3y
4(y + 4)
4 + 3m
m – 7
–c(3c + 5)
5c + 4
t + 3
3(t + 2)
m – n
m + 10n 3
(x – 2)(x + 3)
a – 3b
a + 4b
2b + 4h bh
2h + 2r rh
6v – 7w
3v – 2w
x – 5
4x – 20 4 9 4 9
x – 5
4(x – 5) 1 4
x2 – 9
x + 3
12-3

3. Simplifying Rational Expressions
ALGEBRA 1 LESSON 12-3
54. vertical asymptote: x = 0;
horizontal asymptote: y = 2;
55. vertical asymptote: x = 4;
horizontal asymptote: y = 0;
56. vertical asymptote: x = 0;
horizontal asymptote: y = –4;
58. a2b3c4 b
60.
61. y = x2, y = –2x2, y = 3x2
62. y = x2, y = x2, y = x2
63. y = 0.5x2, y = 2x2, y = –4x2
64. y = –x2, y = 2.3x2, y = –3.8x2 2
5m2 1 4 3 5
12-3