MTH 075 Practice Test 5
Find all values that make the expression undefined.
x2 − 4
1)
x 2 − 13x + 36
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write the rational expression in lowest terms.
2x + 3
2)
6 x + 13x + 6
2x + 3 2x
A) B)
6 x + 13x + 6
2
3x + 2
1 2x + 5
C) D)
3x + 2 3x + 6
Perform the indicated operation and write the answer in lowest terms.
1 4x
3) +
x−4 x+4
4 x 2 − 15 x + 4 4 x 2 − 15 x + 4
A) 2 B)
x + 8 x + 16 x 2 − 16
4 x 2 − 15 x + 4 1 + 4x
C) D)
x 2 − 8 x + 16 (x − 4)(x + 4)
Solve the equation.
x x x
4) + 2 = 2
x − 1 x − 2x − 3 x − 4x + 3
2
A) {5, 0} B) {–3, 0} C) {–5, 0} D) {1, 0}
Divide. Write the answer in lowest terms.
− 3x 3 (4 x )
3
5) ÷
2x6 6x5
64x −9 −9
A) B) C) 64x D)
3 64 x 3 64 x
Write the rational expression in lowest terms.
pq − 5 p + 3q − 15
6)
qr + 4q − 5r − 20
x 2 − 4 x − 12
7)
x 2 − 7 x − 18
z2 − p2
8)
z− p
Multiply. Write the answer in lowest terms.
2 x 2 − 3 x − 9 3x 2 + 13x − 30
9) ⋅
3x 2 − 2 x − 5 x 2 + 3x − 18
5 x − 15 6 x + 12
10) ⋅
12 x + 24 x 30 − 10 x
2
Divide. Write the answer in lowest terms.
2 x 2 − 2 x − 24 5 x 2 − 35 x + 60
11) ÷
x 2 − 7 x + 12 x 2 − 6x + 9
x 2 + 11x + 24 x 2 + 14 x + 48
12) ÷ 2
x 2 + 2x x + 8 x + 12
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Perform the indicated operation. Simplify if possible.
x 2 − 8x 12
13) +
x−2 x−2
x 2 − 8 x + 12
A) B) x + 6 C) x – 6 D) x – 2
x−2
Find the least common denominator (LCD).
1 1
14) , 2
x + 2x x + 4x + 4
2
A) (x + 2)2 B) x(x + 2)2 C) x(x + 2) D) x(x + 1)(x + 2)
Add or subtract. Write the answer in lowest terms.
−5 6
15) −
x−5 5− x
5x − 3 2 x − 9
16) −
8 12
7 5
17) +
x x−3
Perform the indicated operation and write the answer in lowest terms.
x+3 3 4x
18) − 2 +
x x − 10 x x − 10
Solve the equations.
4x 8x − 8 8
19) − =
3 2 3
1 4
20) + =3
x − 3 2x − 6