Solve each equation. See Examples 2 – 5.
18. 19. 20.
21. 22. 23.
24. 25.
26. 27.
28. 29.
30. 31.
32. 33.
34. 35.
36. 37.
38. 39.
40. 41.
42. 43.
44.
45.
46.
47.
48.
Graph each rational function. Give the equations of the vertical and horizontal asymptotes.
See Example 6.
- 54.ƒ 1 x 2 =
1
x+ 2
ƒ 1 x 2 =
1
x- 2
g 1 x 2 =-
2
x
g 1 x 2 =-
1
x
ƒ 1 x 2 =
3
x
ƒ 1 x 2 =
2
x
4 x- 7
4 x^2 - 9
=
+
x+ 1
2 x+ 3
5 x+ 14
x^2 - 9
=
+
2 x+ 4
x- 3
5
p^2 + 3 p+ 2
-
3
p^2 - 4
=
1
p^2 - p- 2
2
k^2 +k- 6
+
1
k^2 - k- 2
=
4
k^2 + 4 k+ 3
5
x- 4
-
3
x- 1
=
x^2 - 1
x^2 - 5 x+ 4
1
x+ 4
+
x
x- 4
=
- 8
x^2 - 16
2 x
x- 3
+
4
x+ 3
=
- 24
x^2 - 9
x
x- 3
+
4
x+ 3
=
18
x^2 - 9
2
r- 5
+
3
2 r+ 1
=
22
2 r^2 - 9 r- 5
6
w+ 3
+
- 7
w- 5
=
- 48
w^2 - 2 w- 15
1
x+ 4
+
1
3
=
- 10
31 x^2 - 162
1
x- 2
+
1
4
=
1
41 x^2 - 42
5
n
+
4
6 - 3 n
=
2 n
6 - 3 n
9
x
+
4
6 x- 3
=
2
6 x- 3
1
t+ 3
+
4
t+ 5
=
2
t^2 + 8 t+ 15
1
y+ 2
+
3
y+ 7
=
5
y^2 + 9 y+ 14
3
x- 2
+
21
x^2 - 4
=
14
x+ 2
3
x+ 2
-
2
x^2 - 4
=
1
x- 2
7
x- 4
+
3
x
=
- 12
x^2 - 4 x
6
x- 4
+
5
x
=
- 20
x^2 - 4 x
3
4 m+ 2
=
17
2
-
7
2 m+ 1
7
6 x+ 3
-
1
3
=
2
2 x+ 1
4
m+ 2
-
11
9
=
1
3 m+ 6
1
y- 1
+
5
12
=
- 2
3 y- 3
4 x- 1
2 x+ 3
=
12 x- 25
6 x- 2
3 x+ 1
x- 4
=
6 x+ 5
2 x- 7
5 x- 8
x+ 2
=
5 x- 1
x+ 3
x- 4
x+ 6
=
2 x+ 3
2 x- 1
x
2
-
12
x
= 1
x
4
-
21
4 x
p+ =- 1
15
p
=- 8
x-
24
x
=- 2
2
3 x
=
6
5 x
+
8
45
3
4 x
=
5
2 x
-
7
4
392 CHAPTER 7 Rational Expressions and Functions
