Download Math 131 EXAM 2 SPRING 2012 Simplify the rational expression

Math 131
EXAM 2
SPRING 2012
Simplify the rational expression. (10 points)
36w - 6w 2
4w4 - 8w3 + 16w 2
2w3 + 16
÷
·
1)
2
2
2
w + 8w + 12
w - 36
9w - 108w + 324
6w(6 - w)
w- 6 w+ 6
2(w 3 + 8)
·
·
w + 6 w + 2 4w2 w 2 - 2w + 4 9(w2 - 12w + 36)
6w(6 - w)
w-6 w+6
2(w + 2) w2 - 2w + 4
·
·
w + 6 w + 2 4w 2 w2 - 2w + 4
9(w - 6) w - 6
-
1
3w
Add or subtract, as indicated, and simplify the result.
x
4
1
+
2)
x 2 - 16 x 2 + 5x + 4 4 + 3x - x 2
(10 points)
x
4
1
(x - 4) x + 4
(x + 4) x + 1
x2 - 3x - 4
x
4
1
(x - 4) x + 4
(x + 4) x + 1
(x - 4)(x + 1)
xx+1
4(x - 4)
x+4
(x - 4) x + 4 x + 1
(x - 4) x + 4 x + 1
(x - 4) x + 4 x + 1
x2 + x
4x - 16
x+4
(x - 4) x + 4 x + 1
(x - 4) x + 4 x + 1
(x - 4) x + 4 x + 1
x 2 - 4x + 12
(x - 4) x + 4 x + 1
Simplify the complex rational expression using Method 1 or Method 2.
7
3
+
8-x x-8 xx-8
-7x + 3x
- 4x
- 4x
4x
x
·
=
=
=
==3)
5
3
xx-8
5(x - 8) + 3x 5x - 40 + 3x 8x - 40
8(x - 5)
2(x - 5)
+
x x-8
1
4)
(- 4x)-1 + 5y-1
-3x -2 - (2y)-2
-
1
5
+
4x y
3
1
x 2 (2y)2
-
1
5
+
4x y
3
1
2
x
4y2
·
4x 2y2
4x 2y2
- xy2 + 20x 2 y
- 12y2 - x 2
- xy(y - 20x)
- (12y2 + x 2)
xy(y - 20x)
12y2 + x 2
Evaluate the expression, if possible by first converting to radical form.
5
4
5/4
5) - 1296 = - 1296 = - 6 5 = - 7776
6) - -
125 -2/3
64 -2
3
=64
125
== -
3
-
125
64
2
=- -
4 2
16
=5
25
Rewrite the expression with a positive rational exponent. Simplify, if possible.
1 3/2
1 3
1
4
=4
=4
=
7) (16-1/4 · 9 3/4)-2 = 161/2 · 9 -3/2 = 4
9
3
27
27
Simplify the expression, if possible. Assume all variables are nonnegative.
35
2
70
70
·
=
=
8)
6
18
2
36
9)
4x 2 - 20x + 25 =
2x - 5 2 = 2x - 5
Simplify the radical expression. Assume that all variables represent positive real numbers.
3 4
2 = 2 1/4 1/3 = 21/12
10)
2
3
3
3
3
3 4
4
5x 2
20x 2
20x 2
=
=
=
11)
25x
5x
3
3
3
25x
5x 2
125x 3
12)
5-2 6
·
5+2 6
5 - 2 6 5 - 4 30 + 4 6
5 - 4 30 + 24 29 - 4 30 4 30 - 29
=
=
=
=
5-46
5 - 24
- 19
19
5-2 6
Simplify the expression. Assume all variables represent positive real numbers.
3
3
3
7 4 3
2
9 5 3
9 3 3
13) 100m n · 600m n = 60000m n = 103 m n · 60n 2 = 10m 3 n 60n 2
Add or subtract. Assume all variables represent positive real numbers.
14) 9 162 - 2 75- 3 98 + 7 108
9 81·2 - 2 25·3- 3 49·2 + 7 36·3
9(9) 2 - 2(5) 3- 3(7) 2 + 7(6) 3
81 2 - 10 3 - 21 2 + 42 3
60 2 + 32 3
Simplify. Write the result in the form a + bi.
15) 6 + -7 (3 - -2)
6 + i 7 (3 - i 2)
18 - 6i 2 + 3i 7 - i 2 14
18 - 6i 2 + 3i 7 + 14
16)
5 - 3i 7 - 2i 35 - 10i - 21i + 6i 2 35 - 31i - 6 29 - 31i 29 31
·
=
=
=
=
i
7 + 2i 7 - 2i
49 + 4
53
53
53 53
3