Question 1

Simplify the expression.
-$\frac { 24 } { 3 m - 12 }$

Accepted Answer

A)  $\frac { 8 } { m - 12 }$ 
B)  $\frac { 8 } { m + 12 }$ 
C)  $\frac { 8 } { m + 4 }$ 
D)  $\frac { 8 } { m - 4 }$ 
A)  $\frac { 8 } { m - 12 }$ 
B)  $\frac { 8 } { m + 12 }$ 
C)  $\frac { 8 } { m + 4 }$ 
D)  $\frac { 8 } { m - 4 }$

Question 2

Perform the indicated operation. Simplify if possible.
-$\frac { 7 } { x - 3 } + \frac { 25 } { 3 - x }$

Accepted Answer

A)  $\frac { 32 } { x - 3 }$ 
B)  $- \frac { 32 } { x - 3 }$ 
C)  $\frac { 18 } { x - 3 }$ 
D)  $- \frac { 18 } { x - 3 }$ 
A)  $\frac { 32 } { x - 3 }$ 
B)  $- \frac { 32 } { x - 3 }$ 
C)  $\frac { 18 } { x - 3 }$ 
D)  $- \frac { 18 } { x - 3 }$

Question 3

Fill in the blank with one of the words or phrases listed below. Not all choices will be used. $$\begin{array} { l l l l } 
\text { least common denominator } & \text { simplifying } & \text { reciprocals } & \text { numerator } \
\text { cross products } & \text { ratio } & \text { proportion } & \text { denominator } \
\text { rational expression } & \text { domain } & \text { complex fraction } & \
\frac { - a } { b } & \frac { a } { - b } & \frac { - a } { - b } &
\end{array}$$
-The of a list of rational expressions is a polynomial of least degree whose factors include all factors of the denominators in the list.

Accepted Answer

A)  reciprocals 
B)  complex fraction 
C)  least common denominator 
D)  rational expression 
A)  reciprocals 
B)  complex fraction 
C)  least common denominator 
D)  rational expression

Question 4

Perform the indicated operation. Simplify if possible.
-$\frac { 7 } { x ^ { 8 } } - 10 x$

Accepted Answer

A)  $\frac { 7 - 10 x ^ { 7 } } { x ^ { 8 } }$ 
B)  $\frac { 7 - 10 x ^ { 9 } } { x ^ { 8 } }$ 
C)  $\frac { 10 x ^ { 9 } - 7 } { x ^ { 8 } }$ 
D)  $\frac { 7 - 10 x } { x ^ { 8 } }$ 
A)  $\frac { 7 - 10 x ^ { 7 } } { x ^ { 8 } }$ 
B)  $\frac { 7 - 10 x ^ { 9 } } { x ^ { 8 } }$ 
C)  $\frac { 10 x ^ { 9 } - 7 } { x ^ { 8 } }$ 
D)  $\frac { 7 - 10 x } { x ^ { 8 } }$

Question 5

Find the quotient and simplify.
-$\frac { 3 b ^ { 2 } x } { 7 b x ^ { 2 } } \div \frac { 21 b ^ { 2 } x ^ { 2 } } { 15 b x }$

Accepted Answer

A)  $\frac { 3 b ^ { 2 } } { 5 }$ 
B)  $\frac { 15 } { 49 x ^ { 2 } }$ 
C)  $\frac { 3 b x } { 5 }$ 
D)  $\frac { 3 } { 5 x ^ { 2 } }$ 
A)  $\frac { 3 b ^ { 2 } } { 5 }$ 
B)  $\frac { 15 } { 49 x ^ { 2 } }$ 
C)  $\frac { 3 b x } { 5 }$ 
D)  $\frac { 3 } { 5 x ^ { 2 } }$

Question 6

Solve the proportion.
-$\frac { 10 } { x } = \frac { 5 } { 2 }$

Accepted Answer

A)  20 
B)  $\frac { 1 } { 4 }$ 
C)  1 
D)  4 
A)  20 
B)  $\frac { 1 } { 4 }$ 
C)  1 
D)  4

Question 7

Simplify.
-$\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }$

Accepted Answer

A)  $\frac { 49 } { x + 7 }$ 
B)  $\frac { x + 7 } { 49 }$ 
C)  $\frac { x - 7 } { 49 }$ 
D)  $\frac { 49 } { x - 7 }$ 
A)  $\frac { 49 } { x + 7 }$ 
B)  $\frac { x + 7 } { 49 }$ 
C)  $\frac { x - 7 } { 49 }$ 
D)  $\frac { 49 } { x - 7 }$

Question 8

Solve the proportion.
-$\frac { x + 6 } { 5 } = \frac { x + 8 } { 7 }$

Accepted Answer

A)  $- 2$ 
B)  $- 1$ 
C)  1 
D)  2 
A)  $- 2$ 
B)  $- 1$ 
C)  1 
D)  2

Question 9

Simplify the expression.
-$\frac { - 6 x + 6 y } { - 6 y + 6 x }$

Accepted Answer

A)  6 
B)  $- 1$ 
C)  -6 
D)  1 
A)  6 
B)  $- 1$ 
C)  -6 
D)  1

Question 10

Simplify.
-$\frac { \frac { 2 } { y } } { \frac { 7 } { y + 6 } }$

Accepted Answer

A)  $\frac { 7 y } { 2 ( y + 6 ) }$ 
B)  $\frac { 2 ( y + 6 ) } { 7 y }$ 
C)  $14 y ( y + 6 )$ 
D)  $\frac { y + 6 } { 14 y }$ 
A)  $\frac { 7 y } { 2 ( y + 6 ) }$ 
B)  $\frac { 2 ( y + 6 ) } { 7 y }$ 
C)  $14 y ( y + 6 )$ 
D)  $\frac { y + 6 } { 14 y }$

Question 11

Perform the indicated operation and simplify if possible.
-$\frac { y ^ { 2 } - 9 y + 18 } { 3 y + 9 } \cdot \frac { y + 3 } { 4 y - 24 }$

Accepted Answer

A)  $\frac { y - 6 } { 12 }$ 
B)  $\frac { y + 3 } { 12 }$ 
C)  $\frac { y - 3 } { 12 }$ 
D)  $\frac { ( y - 3 ) ( y - 6 ) } { 12 ( y + 6 ) }$ 
A)  $\frac { y - 6 } { 12 }$ 
B)  $\frac { y + 3 } { 12 }$ 
C)  $\frac { y - 3 } { 12 }$ 
D)  $\frac { ( y - 3 ) ( y - 6 ) } { 12 ( y + 6 ) }$

Question 12

Find the quotient and simplify.
-$\frac { x - 8 } { - 5 - x } \div \frac { x ^ { 2 } + 7 x - 8 } { x ^ { 2 } + 13 x + 40 }$

Accepted Answer

A)  $- \frac { x - 8 } { x - 1 }$ 
B)  $\frac { x + 8 } { x - 1 }$ 
C)  $- \frac { ( x - 8 ) ( x + 8 ) } { ( x + 5 ) ^ { 2 } }$ 
D)  $- \frac { x + 8 } { x - 1 }$ 
A)  $- \frac { x - 8 } { x - 1 }$ 
B)  $\frac { x + 8 } { x - 1 }$ 
C)  $- \frac { ( x - 8 ) ( x + 8 ) } { ( x + 5 ) ^ { 2 } }$ 
D)  $- \frac { x + 8 } { x - 1 }$

Question 13

Perform the indicated operation. Simplify if possible.
-$\frac { x + 5 } { x ^ { 2 } + 5 x - 14 } + \frac { 5 x + 8 } { x ^ { 2 } + 11 x + 28 }$

Accepted Answer

A)  $\frac { 6 x ^ { 2 } + 7 x + 4 } { ( x - 7 ) ( x + 2 ) ( x - 4 ) }$ 
B)  $6 x + 13$ 
C)  $\frac { 6 x ^ { 2 } + 7 x + 4 } { ( x + 7 ) ( x - 2 ) ( x + 4 ) }$ 
D)  $\frac { 6 x + 13 } { 2 x ^ { 2 } + 16 x + 14 }$ 
A)  $\frac { 6 x ^ { 2 } + 7 x + 4 } { ( x - 7 ) ( x + 2 ) ( x - 4 ) }$ 
B)  $6 x + 13$ 
C)  $\frac { 6 x ^ { 2 } + 7 x + 4 } { ( x + 7 ) ( x - 2 ) ( x + 4 ) }$ 
D)  $\frac { 6 x + 13 } { 2 x ^ { 2 } + 16 x + 14 }$

Question 14

Provide an appropriate response.
-For a certain computer desk, the manufacturing cost C per desk (in dollars) is
 
where $\mathrm { x }$ is the number of desks manufactured.
a. Find the average cost per desk when manufacturing 200 desks.
b. Find the average cost per desk when manufacturing 1000 desks.

Accepted Answer

A)  a. $\$ 220$; b. $\$ 204$ 
B)  a. $\$ 180$; b. $\$ 196$ 
C)  a. $\$ 240$; b. $\$ 220$ 
D)  a. $\$ 40 ;$ b. $\$ 24$ 
A)  a. $\$ 220$; b. $\$ 204$ 
B)  a. $\$ 180$; b. $\$ 196$ 
C)  a. $\$ 240$; b. $\$ 220$ 
D)  a. $\$ 40 ;$ b. $\$ 24$

Question 15

Solve.
-There are $1.1$ milligrams of iron in a $3.5$ ounce serving of chicken. How much iron is in 9 ounces of chicken? Round the answer to one decimal place.

Accepted Answer

A)  $2.4 \mathrm { mg }$ 
B)  $0.4 \mathrm { mg }$ 
C)  $3.8 \mathrm { mg }$ 
D)  $2.8 \mathrm { mg }$ 
A)  $2.4 \mathrm { mg }$ 
B)  $0.4 \mathrm { mg }$ 
C)  $3.8 \mathrm { mg }$ 
D)  $2.8 \mathrm { mg }$

Question 16

Simplify the expression.
-$\frac { 36 - x ^ { 2 } } { x ^ { 2 } - 13 x + 42 }$

Accepted Answer

A)  $- \frac { x - 6 } { x - 7 }$ 
B)  $- \frac { x + 6 } { x + 7 }$ 
C)  $- \frac { x + 6 } { x - 7 }$ 
D)  $\frac { x + 6 } { x - 7 }$ 
A)  $- \frac { x - 6 } { x - 7 }$ 
B)  $- \frac { x + 6 } { x + 7 }$ 
C)  $- \frac { x + 6 } { x - 7 }$ 
D)  $\frac { x + 6 } { x - 7 }$

Question 17

Simplify the expression.
-$\frac { 7 - m } { m - 7 }$

Accepted Answer

A)  $- \mathrm { m }$ 
B)  $- 1$ 
C)  1 
D)  can't simplify 
A)  $- \mathrm { m }$ 
B)  $- 1$ 
C)  1 
D)  can't simplify

Question 18

Perform the indicated operation. Simplify if possible.
-$\frac { x ^ { 2 } + x } { 3 } \cdot \frac { 9 } { x + 1 }$

Accepted Answer

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

Question 19

Simplify the expression.
-$\frac { 4 x - 8 } { 10 - 5 x }$

Accepted Answer

A)  $- 1$ 
B)  1 
C)  $\frac { 4 } { 5 }$ 
D)  $- \frac { 4 } { 5 }$ 
A)  $- 1$ 
B)  1 
C)  $\frac { 4 } { 5 }$ 
D)  $- \frac { 4 } { 5 }$

Question 20

Solve.
-Mark and Rachel both work for Smith Landscaping Company. Mark can finish a planting job in 3 hours, while it takes Rachel 4 hours to finish the same job. If Mark and Rachel will work together on the job, and the cost of labor is $\$ 35$ per hour, what should the labor estimate be? (Round to the nearest cent, if necessary.)

Accepted Answer

A)  $\$ 60.00$ 
B)  $\$ 20.42$ 
C)  $\$ 122.50$ 
D)  $\$ 120.00$ 
A)  $\$ 60.00$ 
B)  $\$ 20.42$ 
C)  $\$ 122.50$ 
D)  $\$ 120.00$

Simplify the expression. - $\frac { 24 } { 3 m - 12 }$

Perform the indicated operation. Simplify if possible. - $\frac { 7 } { x - 3 } + \frac { 25 } { 3 - x }$

Perform the indicated operation. Simplify if possible. - $\frac { 7 } { x ^ { 8 } } - 10 x$

Find the quotient and simplify. - $\frac { 3 b ^ { 2 } x } { 7 b x ^ { 2 } } \div \frac { 21 b ^ { 2 } x ^ { 2 } } { 15 b x }$

Solve the proportion. - $\frac { 10 } { x } = \frac { 5 } { 2 }$

Simplify. - $\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }$

Solve the proportion. - $\frac { x + 6 } { 5 } = \frac { x + 8 } { 7 }$

Simplify the expression. - $\frac { - 6 x + 6 y } { - 6 y + 6 x }$

Simplify. - $\frac { \frac { 2 } { y } } { \frac { 7 } { y + 6 } }$

Perform the indicated operation and simplify if possible. - $\frac { y ^ { 2 } - 9 y + 18 } { 3 y + 9 } \cdot \frac { y + 3 } { 4 y - 24 }$

Find the quotient and simplify. - $\frac { x - 8 } { - 5 - x } \div \frac { x ^ { 2 } + 7 x - 8 } { x ^ { 2 } + 13 x + 40 }$

Perform the indicated operation. Simplify if possible. - $\frac { x + 5 } { x ^ { 2 } + 5 x - 14 } + \frac { 5 x + 8 } { x ^ { 2 } + 11 x + 28 }$

Solve. -There are $1.1$ milligrams of iron in a $3.5$ ounce serving of chicken. How much iron is in 9 ounces of chicken? Round the answer to one decimal place.

Simplify the expression. - $\frac { 36 - x ^ { 2 } } { x ^ { 2 } - 13 x + 42 }$

Simplify the expression. - $\frac { 7 - m } { m - 7 }$

Perform the indicated operation. Simplify if possible. - $\frac { x ^ { 2 } + x } { 3 } \cdot \frac { 9 } { x + 1 }$

Simplify the expression. - $\frac { 4 x - 8 } { 10 - 5 x }$

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

Simplify the expression. - 243m−12\frac { 24 } { 3 m - 12 }3m−1224​

Perform the indicated operation. Simplify if possible. - 7x−3+253−x\frac { 7 } { x - 3 } + \frac { 25 } { 3 - x }x−37​+3−x25​

Perform the indicated operation. Simplify if possible. - 7x8−10x\frac { 7 } { x ^ { 8 } } - 10 xx87​−10x

Find the quotient and simplify. - 3b2x7bx2÷21b2x215bx\frac { 3 b ^ { 2 } x } { 7 b x ^ { 2 } } \div \frac { 21 b ^ { 2 } x ^ { 2 } } { 15 b x }7bx23b2x​÷15bx21b2x2​

Solve the proportion. - 10x=52\frac { 10 } { x } = \frac { 5 } { 2 }x10​=25​

Simplify. - x49−1x1+7x\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }1+x7​49x​−x1​​

Solve the proportion. - x+65=x+87\frac { x + 6 } { 5 } = \frac { x + 8 } { 7 }5x+6​=7x+8​

Simplify the expression. - −6x+6y−6y+6x\frac { - 6 x + 6 y } { - 6 y + 6 x }−6y+6x−6x+6y​

Simplify. - 2y7y+6\frac { \frac { 2 } { y } } { \frac { 7 } { y + 6 } }y+67​y2​​

Perform the indicated operation and simplify if possible. - y2−9y+183y+9⋅y+34y−24\frac { y ^ { 2 } - 9 y + 18 } { 3 y + 9 } \cdot \frac { y + 3 } { 4 y - 24 }3y+9y2−9y+18​⋅4y−24y+3​

Find the quotient and simplify. - x−8−5−x÷x2+7x−8x2+13x+40\frac { x - 8 } { - 5 - x } \div \frac { x ^ { 2 } + 7 x - 8 } { x ^ { 2 } + 13 x + 40 }−5−xx−8​÷x2+13x+40x2+7x−8​

Perform the indicated operation. Simplify if possible. - x+5x2+5x−14+5x+8x2+11x+28\frac { x + 5 } { x ^ { 2 } + 5 x - 14 } + \frac { 5 x + 8 } { x ^ { 2 } + 11 x + 28 }x2+5x−14x+5​+x2+11x+285x+8​

Solve. -There are 1.11.11.1 milligrams of iron in a 3.53.53.5 ounce serving of chicken. How much iron is in 9 ounces of chicken? Round the answer to one decimal place.

Simplify the expression. - 36−x2x2−13x+42\frac { 36 - x ^ { 2 } } { x ^ { 2 } - 13 x + 42 }x2−13x+4236−x2​

Simplify the expression. - 7−mm−7\frac { 7 - m } { m - 7 }m−77−m​

Perform the indicated operation. Simplify if possible. - x2+x3⋅9x+1\frac { x ^ { 2 } + x } { 3 } \cdot \frac { 9 } { x + 1 }3x2+x​⋅x+19​

Simplify the expression. - 4x−810−5x\frac { 4 x - 8 } { 10 - 5 x }10−5x4x−8​