Question 1

Find the product and simplify.
-$\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 3 x } { - 33 x - 33 }$

Accepted Answer

A)  $- \frac { x ^ { 2 } + 1 } { 11 }$ 
B)  $- \frac { x ^ { 3 } + 1 } { 11 ( x + 1 ) }$ 
C)  $\frac { x + 1 } { 11 ( - x - 1 ) }$ 
D)  $- \frac { 1 } { 11 }$ 
A)  $- \frac { x ^ { 2 } + 1 } { 11 }$ 
B)  $- \frac { x ^ { 3 } + 1 } { 11 ( x + 1 ) }$ 
C)  $\frac { x + 1 } { 11 ( - x - 1 ) }$ 
D)  $- \frac { 1 } { 11 }$

Question 2

Simplify the expression.
-$\frac { a ^ { 2 } - a b + 8 a - 8 b } { a + 8 }$

Accepted Answer

A)  $\frac { 1 } { a + 8 }$ 
B)  $a - b$ 
C)  $\frac { a ^ { 2 } - a b + 8 a - 8 b } { a + 8 }$ 
D)  $a - 2 b + 1$ 
A)  $\frac { 1 } { a + 8 }$ 
B)  $a - b$ 
C)  $\frac { a ^ { 2 } - a b + 8 a - 8 b } { a + 8 }$ 
D)  $a - 2 b + 1$

Question 3

Solve the problem.
-A gas law in chemistry says that $\frac { P V } { T } = \frac { p v } { t }$. If $T = 320 , t = 360 , V = 8 , P = 20$, and $v = 5$, find the value of p. Round to the nearest thousandth.

Accepted Answer

A)  36 
B)  128 
C)  $3.6$ 
D)  $0.1$ 
A)  36 
B)  128 
C)  $3.6$ 
D)  $0.1$

Question 4

Perform the indicated operation. Simplify if possible.
-$\frac { 7 y ^ { 2 } } { y - 1 } - \frac { 7 y } { y - 1 }$

Accepted Answer

A)  $\frac { 7 y } { y - 1 }$ 
B)  0 
C)  $\frac { 7 y ( y + 1 ) } { y - 1 }$ 
D)  $7 \mathrm { y }$ 
A)  $\frac { 7 y } { y - 1 }$ 
B)  0 
C)  $\frac { 7 y ( y + 1 ) } { y - 1 }$ 
D)  $7 \mathrm { y }$

Question 5

Simplify the expression.
-$\frac { 5 x ^ { 2 } + 15 x ^ { 3 } } { 3 x + 9 x ^ { 2 } }$

Accepted Answer

A)  $\frac { 5 + 15 x ^ { 3 } } { 3 x + 9 }$ 
B)  $\frac { 5 x ^ { 2 } + 15 x ^ { 3 } } { 3 x + 9 x ^ { 2 } }$ 
C)  $\frac { 5 x } { 3 }$ 
D)  $\frac { 5 } { 3 }$ 
A)  $\frac { 5 + 15 x ^ { 3 } } { 3 x + 9 }$ 
B)  $\frac { 5 x ^ { 2 } + 15 x ^ { 3 } } { 3 x + 9 x ^ { 2 } }$ 
C)  $\frac { 5 x } { 3 }$ 
D)  $\frac { 5 } { 3 }$

Question 6

Multiply or divide as indicated.
-$\frac { x ^ { 2 } - 16 } { 4 y } \div \frac { 4 - x } { 8 x y }$

Accepted Answer

A)  $- 2 x ( x - 4 )$ 
B)  $2 x ( x + 4 )$ 
C)  $2 x ( x - 4 )$ 
D)  $- 2 x ( x + 4 )$ 
A)  $- 2 x ( x - 4 )$ 
B)  $2 x ( x + 4 )$ 
C)  $2 x ( x - 4 )$ 
D)  $- 2 x ( x + 4 )$

Question 7

Find the quotient and simplify.
-$\frac { ( y - 3 ) ^ { 2 } } { 12 } \div \frac { 12 y - 36 } { 144 }$

Accepted Answer

A)  $\frac { 12 ( y - 3 ) ^ { 2 } } { 12 y - 36 }$ 
B)  $\frac { ( y - 3 ) ^ { 3 } } { 144 }$ 
C)  $\frac { 1 } { y - 3 }$ 
D)  $y - 3$ 
A)  $\frac { 12 ( y - 3 ) ^ { 2 } } { 12 y - 36 }$ 
B)  $\frac { ( y - 3 ) ^ { 3 } } { 144 }$ 
C)  $\frac { 1 } { y - 3 }$ 
D)  $y - 3$

Question 8

Simplify.
-$\frac { \frac { x + 1 } { 5 } } { \frac { 3 x - 1 } { 20 } }$

Accepted Answer

A)  $\frac { 4 ( x + 1 ) } { 3 x - 1 }$ 
B)  $\frac { ( x + 1 ) ( 3 x - 1 ) } { 4 }$ 
C)  $\frac { ( x + 1 ) ( 3 x - 1 ) } { 20 }$ 
D)  $\frac { 4 ( x + 1 ) } { 3 ( x - 1 ) }$ 
A)  $\frac { 4 ( x + 1 ) } { 3 x - 1 }$ 
B)  $\frac { ( x + 1 ) ( 3 x - 1 ) } { 4 }$ 
C)  $\frac { ( x + 1 ) ( 3 x - 1 ) } { 20 }$ 
D)  $\frac { 4 ( x + 1 ) } { 3 ( x - 1 ) }$

Question 9

Solve the equation.
-$\frac { x } { 6 } - 4 = 1$

Accepted Answer

A)  $- 30$ 
B)  30 
C)  18 
D)  $- 18$ 
A)  $- 30$ 
B)  30 
C)  18 
D)  $- 18$

Question 10

Solve the equation.
-$\frac { m + 5 } { m ^ { 2 } + 5 m + 4 } - \frac { 5 } { m ^ { 2 } + 2 m + 1 } = \frac { m - 5 } { m ^ { 2 } + 5 m + 4 }$

Accepted Answer

A)  no solution 
B)  10 
C)  2 
D)  $- 2$ 
A)  no solution 
B)  10 
C)  2 
D)  $- 2$

Question 11

Solve the equation.
-$\frac { x } { 10 } - \frac { 1 } { 5 } = \frac { x + 9 } { 5 }$

Accepted Answer

A)  $- 10$ 
B)  $- 19$ 
C)  $- 11$ 
D)  $- 20$ 
A)  $- 10$ 
B)  $- 19$ 
C)  $- 11$ 
D)  $- 20$

Question 12

Solve.
-One pump can drain a pool in 12 minutes. When a second pump is also used, the pool only takes 4 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use?

Accepted Answer

A)  $6 \mathrm {~min}$ 
B)  $40 \mathrm {~min}$ 
C)  $\frac { 1 } { 6 } \min$ 
D)  $3 \mathrm {~min}$ 
A)  $6 \mathrm {~min}$ 
B)  $40 \mathrm {~min}$ 
C)  $\frac { 1 } { 6 } \min$ 
D)  $3 \mathrm {~min}$

Question 13

Solve the problem.
-If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 600 } { x + 20 }$, what is the cost per unit if 10 units of plywood are produced?

Accepted Answer

A)  $\$ 40.00$ 
B)  $\$ 3.00$ 
C)  $\$ 20.00$ 
D)  $\$ 60.00$ 
A)  $\$ 40.00$ 
B)  $\$ 3.00$ 
C)  $\$ 20.00$ 
D)  $\$ 60.00$

Question 14

Solve the equation for the indicated variable.
-$P = \frac { A } { 1 + r t } \quad$ for $r$

Accepted Answer

A)  $r = \frac { P - 1 } { \text { At } }$ 
B)  $r = \frac { A - P } { P t }$ 
C)  $r = P - A t$ 
D)  $r = \frac { P - A } { 1 + t }$ 
A)  $r = \frac { P - 1 } { \text { At } }$ 
B)  $r = \frac { A - P } { P t }$ 
C)  $r = P - A t$ 
D)  $r = \frac { P - A } { 1 + t }$

Question 15

Simplify the rational expression.
-$\frac { 2 m ^ { 3 } - 2 m ^ { 2 } - 12 m } { m ^ { 2 } - 5 m + 6 }$

Accepted Answer

A)  $2 \mathrm {~m}$ 
B)  $\frac { 2 m ( m + 3 ) } { ( m - 3 ) }$ 
C)  $\frac { 2 m ( m + 2 ) } { ( m - 2 ) }$ 
D)  $\frac { 2 m ( m - 3 ) ( m + 2 ) } { ( m + 3 ) ( m - 2 ) }$ 
A)  $2 \mathrm {~m}$ 
B)  $\frac { 2 m ( m + 3 ) } { ( m - 3 ) }$ 
C)  $\frac { 2 m ( m + 2 ) } { ( m - 2 ) }$ 
D)  $\frac { 2 m ( m - 3 ) ( m + 2 ) } { ( m + 3 ) ( m - 2 ) }$

Question 16

Solve.
-The ratio of the weight of an object on Earth to the weight of the same object on Pluto is 100 to 3 . If a buffalo weighs 3905 pounds on Earth, find the buffalo's weight on Pluto. (Round to the nearest pound.)

Accepted Answer

A)  $117 \mathrm { lb }$ 
B)  $8 \mathrm { lb }$ 
C)  $1,171,500 \mathrm { lb }$ 
D)  $11,715 \mathrm { lb }$ 
A)  $117 \mathrm { lb }$ 
B)  $8 \mathrm { lb }$ 
C)  $1,171,500 \mathrm { lb }$ 
D)  $11,715 \mathrm { lb }$

Question 17

Solve the equation.
-$\frac { x - 6 } { 2 } = \frac { x + 3 } { 6 }$

Accepted Answer

A)  $\frac { 21 } { 2 }$ 
B)  3 
C)  8 
D)  $\frac { 7 } { 2 }$ 
A)  $\frac { 21 } { 2 }$ 
B)  3 
C)  8 
D)  $\frac { 7 } { 2 }$

Question 18

Solve the problem.
-A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, $C ( t )$, in milligrams after t hours is modeled by $C ( t ) = \frac { 6 t } { 2 t ^ { 2 } + 2 }$. Estimate the drug's concentration after 4 hours. (Round to the nearest hundredth.)

Accepted Answer

A)  $0.71 \mathrm { mg }$ 
B)  $2.40 \mathrm { mg }$ 
C)  $2.34 \mathrm { mg }$ 
D)  $0.65 \mathrm { mg }$ 
A)  $0.71 \mathrm { mg }$ 
B)  $2.40 \mathrm { mg }$ 
C)  $2.34 \mathrm { mg }$ 
D)  $0.65 \mathrm { mg }$

Question 19

Simplify.
-$\frac { - 6 x ^ { - 1 } - 5 y ^ { - 1 } } { - 5 x ^ { - 2 } + 3 y ^ { - 2 } }$

Accepted Answer

A)  $\frac { - 5 y ^ { 2 } + 3 x ^ { 2 } } { - 6 x y ^ { 2 } - 5 x ^ { 2 } y }$ 
B)  $\frac { - 5 x ^ { 2 } + 3 y ^ { 2 } } { - 6 x - 5 y }$ 
C)  $\frac { 6 x y ^ { 2 } + 5 x ^ { 2 } y } { 5 y ^ { 2 } + 3 x ^ { 2 } }$ 
D)  $\frac { - 6 x y ^ { 2 } - 5 x ^ { 2 } y } { - 5 y ^ { 2 } + 3 x ^ { 2 } }$ 
A)  $\frac { - 5 y ^ { 2 } + 3 x ^ { 2 } } { - 6 x y ^ { 2 } - 5 x ^ { 2 } y }$ 
B)  $\frac { - 5 x ^ { 2 } + 3 y ^ { 2 } } { - 6 x - 5 y }$ 
C)  $\frac { 6 x y ^ { 2 } + 5 x ^ { 2 } y } { 5 y ^ { 2 } + 3 x ^ { 2 } }$ 
D)  $\frac { - 6 x y ^ { 2 } - 5 x ^ { 2 } y } { - 5 y ^ { 2 } + 3 x ^ { 2 } }$

Question 20

Given that the pair of triangles are similar, find x.
-

Accepted Answer

A)  $x = 19$ 
B)  $x = 20$ 
C)  $x = 25$ 
D)  $x = 12$ 
A)  $x = 19$ 
B)  $x = 20$ 
C)  $x = 25$ 
D)  $x = 12$

Find the product and simplify. - $\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 3 x } { - 33 x - 33 }$

Simplify the expression. - $\frac { a ^ { 2 } - a b + 8 a - 8 b } { a + 8 }$

Solve the problem. -A gas law in chemistry says that $\frac { P V } { T } = \frac { p v } { t }$ . If $T = 320 , t = 360 , V = 8 , P = 20$ , and $v = 5$ , find the value of p. Round to the nearest thousandth.

Perform the indicated operation. Simplify if possible. - $\frac { 7 y ^ { 2 } } { y - 1 } - \frac { 7 y } { y - 1 }$

Simplify the expression. - $\frac { 5 x ^ { 2 } + 15 x ^ { 3 } } { 3 x + 9 x ^ { 2 } }$

Multiply or divide as indicated. - $\frac { x ^ { 2 } - 16 } { 4 y } \div \frac { 4 - x } { 8 x y }$

Find the quotient and simplify. - $\frac { ( y - 3 ) ^ { 2 } } { 12 } \div \frac { 12 y - 36 } { 144 }$

Simplify. - $\frac { \frac { x + 1 } { 5 } } { \frac { 3 x - 1 } { 20 } }$

Solve the equation. - $\frac { x } { 6 } - 4 = 1$

Solve the equation. - $\frac { m + 5 } { m ^ { 2 } + 5 m + 4 } - \frac { 5 } { m ^ { 2 } + 2 m + 1 } = \frac { m - 5 } { m ^ { 2 } + 5 m + 4 }$

Solve the equation. - $\frac { x } { 10 } - \frac { 1 } { 5 } = \frac { x + 9 } { 5 }$

Solve. -One pump can drain a pool in 12 minutes. When a second pump is also used, the pool only takes 4 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use?

Solve the problem. -If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 600 } { x + 20 }$ , what is the cost per unit if 10 units of plywood are produced?

Solve the equation for the indicated variable. - $P = \frac { A } { 1 + r t } \quad$ for $r$

Simplify the rational expression. - $\frac { 2 m ^ { 3 } - 2 m ^ { 2 } - 12 m } { m ^ { 2 } - 5 m + 6 }$

Solve. -The ratio of the weight of an object on Earth to the weight of the same object on Pluto is 100 to 3 . If a buffalo weighs 3905 pounds on Earth, find the buffalo's weight on Pluto. (Round to the nearest pound.)

Solve the equation. - $\frac { x - 6 } { 2 } = \frac { x + 3 } { 6 }$

Simplify. - $\frac { - 6 x ^ { - 1 } - 5 y ^ { - 1 } } { - 5 x ^ { - 2 } + 3 y ^ { - 2 } }$

Given that the pair of triangles are similar, find x. -

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Rational Expressions

Find the product and simplify. - x3+1x3−x2+x⋅3x−33x−33\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 3 x } { - 33 x - 33 }x3−x2+xx3+1​⋅−33x−333x​

Simplify the expression. - a2−ab+8a−8ba+8\frac { a ^ { 2 } - a b + 8 a - 8 b } { a + 8 }a+8a2−ab+8a−8b​

Solve the problem. -A gas law in chemistry says that PVT=pvt\frac { P V } { T } = \frac { p v } { t }TPV​=tpv​ . If T=320,t=360,V=8,P=20T = 320 , t = 360 , V = 8 , P = 20T=320,t=360,V=8,P=20 , and v=5v = 5v=5 , find the value of p. Round to the nearest thousandth.

Perform the indicated operation. Simplify if possible. - 7y2y−1−7yy−1\frac { 7 y ^ { 2 } } { y - 1 } - \frac { 7 y } { y - 1 }y−17y2​−y−17y​

Simplify the expression. - 5x2+15x33x+9x2\frac { 5 x ^ { 2 } + 15 x ^ { 3 } } { 3 x + 9 x ^ { 2 } }3x+9x25x2+15x3​

Multiply or divide as indicated. - x2−164y÷4−x8xy\frac { x ^ { 2 } - 16 } { 4 y } \div \frac { 4 - x } { 8 x y }4yx2−16​÷8xy4−x​

Find the quotient and simplify. - (y−3)212÷12y−36144\frac { ( y - 3 ) ^ { 2 } } { 12 } \div \frac { 12 y - 36 } { 144 }12(y−3)2​÷14412y−36​

Simplify. - x+153x−120\frac { \frac { x + 1 } { 5 } } { \frac { 3 x - 1 } { 20 } }203x−1​5x+1​​

Solve the equation. - x6−4=1\frac { x } { 6 } - 4 = 16x​−4=1

Solve the equation. - m+5m2+5m+4−5m2+2m+1=m−5m2+5m+4\frac { m + 5 } { m ^ { 2 } + 5 m + 4 } - \frac { 5 } { m ^ { 2 } + 2 m + 1 } = \frac { m - 5 } { m ^ { 2 } + 5 m + 4 }m2+5m+4m+5​−m2+2m+15​=m2+5m+4m−5​

Solve the equation. - x10−15=x+95\frac { x } { 10 } - \frac { 1 } { 5 } = \frac { x + 9 } { 5 }10x​−51​=5x+9​