Algebra WA7
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School
Thomas Edison State College *
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Course
115
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
6
Uploaded by KidBadgerPerson643
Christian Jensen
Professor Smith
MAT-115: INTERMEDIATE ALGEBRA
12 April 2023
Written Assignment 7 (Answer key only) - Proof of work attached
7.1: Multiply and Divide Rational Expressions
Determine the values for which the rational expression is undefined.
1.
x
−
3
2
x
+
10
2x+10=0
2x=-10
X=-5 undefined
2.
x
x
2
−
4
x² - 4 = 0
x² = 4
x = 2 or (-2)
If x = 2 or -2 the rational expression is undefined
3.
x
+
5
x
2
+
4
x
+
4
x² + 4x + 4 = 0
(x +2)(x + 2) = 0
x + 2 = 0
x = -2
If x = -2 the rational expression is undefined
Simplify the rational expression.
4.
x
2
−
9
x
2
−
6
x
+
9
(x+3) / (x−3)
5.
x
2
−
2
x
−
3
x
2
−
5
x
+
6
(x+1) / (x−2)
6.
x
2
−
4
x
+
4
x
2
−
2
x
(x-2) / (x)
Multiply and reduce to lowest terms.
7.
x
x
2
−
x
−
20
⋅
x
2
−
25
5
x(x+5) / 5(x+4)
8.
x
2
+
3
x
x
2
−
2
x
+
8
⋅
x
−
4
x
2
(x+3)(x−4) / 2x(x−2x+8)
9.
6
x
x
2
+
8
x
−
9
⋅
x
2
−
1
x
2
6(x+1) / x(x+9)
Divide and reduce to lowest terms.
10.
2
x
2
−
10
x
x
2
+
10
x
+
25
÷
x
−
5
x
+
5
2x / x+5
11.
x
−
6
8
x
+
32
÷
x
2
−
36
x
2
+
10
x
+
24
1/8
Solve.
12.
Given
f
(
x
)=
x
2
+
10
x
+
25
x
−
4
and
g
(
x
)=
4
−
x
x
2
−
25
, find
f
(
x
)
⋅
g
(
x
)
.
x+5 / x−5
13.
Given
f
(
x
)=
x
2
−
9
x
−
3
and
g
(
x
)=
x
3
−
27
3
x
2
+
9
x
+
27
, find
f
(
x
)
÷g
(
x
)
.
3(x+3) / x−3
14.
Given
f
(
x
)=
x
2
+
5
x
+
6
x
2
−
9
and
g
(
x
)=
4
x
+
8
x
2
−
6
x
+
9
, find
f
(
x
)
÷g
(
x
)
.
(x−3) / 4 = x/4 - 3/4
7.2: Add and Subtract Rational Expressions
Simplify.
15.
x
2
+
12
x
x
+
6
+
36
x
+
6
x+6
16.
x
2
x
+
10
−
100
x
+
10
x-10
17.
7
x
x
2
−
25
−
35
x
2
−
25
7 / x+2
18.
x
2
x
−
7
+
49
7
−
x
x+7
19.
x
2
−
8
x
x
−
10
+
20
10
−
x
x+2
20.
4
x
2
2
x
−
1
+
1
1
−
2
x
2x+1
Find the lowest common denominator.
21.
5
x
x
−
4
+
7
x
+
4
5x^2+27x−28 / (x−4)(x+4)
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22.
5
x
2
x
−
10
+
5
x
+
2
x
2
+
x
−
30
5x^2+40x+4 / 2(x−5)(x+6)
23.
5
x
x
−
4
+
3
x
−
6
x
2
−
8
x
+
16
(x-4)
Solve.
24.
5
x
−
4
+
3
x
+
4
(8x+8) / (x−4)(x+4)=8(x+1)/(x−4)(x+4)
25.
2
x
−
4
−
3
x
2
−
x
−
12
2x+3 / (x−4)(x+3)
26.
5
x
−
4
+
3
x
2
−
8
x
+
16
(5x-17) / (x-4)(x-4)
27.
Given
f
(
x
)=
5
x
+
4
and
g
(
x
)=
3
x
−
4
, find
f
(
x
)+
g
(
x
)
.
8(x−1) / (x+4)(x−4)
28.
Given
f
(
x
)=
6
x
−
5
and
g
(
x
)=
1
x
2
−
4
x
−
5
, find
f
(
x
)−
g
(
x
)
.
6x+5 / (x−5)(x+1)
29.
Given
f
(
x
)=
1
2
x
−
8
and
g
(
x
)=
3
x
2
−
8
x
+
16
, find
f
(
x
)−
g
(
x
)
.
(x-10) / 2(x-4)^2
7.3: Simplify Complex Rational Expressions
Simplify.
30.
5
x
x
−
4
10
x
2
−
8
x
+
16
First step: write expression as a fraction divided by a fraction.
x(x−4) / 2
31.
5
x
2
x
−
4
15
x
x
2
−
16
First step: write expression as a fraction divided by a fraction.
x(x+4) / 3
32.
3
x
2
+
3
x
−
10
12
x
x
+
5
First step: write expression as a fraction divided by a fraction.
1 / (x−2)4x
7.4: Solve Rational Equations
Solve.
33.
3
x
−
2
+
1
x
+
2
=
12
x
2
−
4
No Solution
34.
4
2
x
−
1
−
2
2
x
+
1
=
14
4
x
2
−
1
x=2
35.
3
x
−
1
+
1
x
−
2
=
13
x
2
−
3
x
+
2
x=5
State the domain.
36.
x
−
3
x
2
(−∞ ,0)∪(0,∞)
37.
x
−
3
x
2
−
25
(−∞, −5)∪(−5, 5)∪(5,∞)
38.
x
−
3
x
2
+
7
x
+
12
(−∞, −4)∪(−4, −3)∪(−3, ∞)
Solve for the variable indicated.
39.
y
=
3
x
−
9
for
x.
y/3 + 3 = x
40.
A
=
bh
2
for
b.
2A/h = b
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