Question 1

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { x ^ { 2 } - 2 x + 6 x - 12 } { 2 x ^ { 2 } + 9 x + 12 x + 54 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } - 8 x - 12 } { 2 x ^ { 2 } + 21 x + 54 }$ 
B)  $\frac { x - 2 } { x + 6 }$ 
C)  $\frac { x - 2 } { 2 x + 9 }$ 
D)  $\frac { x + 6 } { 2 x + 9 }$ 
A)  $\frac { x ^ { 2 } - 8 x - 12 } { 2 x ^ { 2 } + 21 x + 54 }$ 
B)  $\frac { x - 2 } { x + 6 }$ 
C)  $\frac { x - 2 } { 2 x + 9 }$ 
D)  $\frac { x + 6 } { 2 x + 9 }$

Question 2

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-x2 - 16 x2 - 11x + 28

Accepted Answer

A)  x = 0 
B)  x = -7, x = -4 
C)  x = 4, x = -4 
D)  x = 7, x = 4 
A)  x = 0 
B)  x = -7, x = -4 
C)  x = 4, x = -4 
D)  x = 7, x = 4

Question 3

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { 6 } { a + 3 }$$

Accepted Answer

A)  $a = - 3$ 
B)  $a = 0$ 
C)  $a = 3$ 
D)  Defined for all real numbers 
A)  $a = - 3$ 
B)  $a = 0$ 
C)  $a = 3$ 
D)  Defined for all real numbers

Question 4

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { 6 } { x - 3 } + \frac { 6 } { 3 - x }$$

Accepted Answer

A)  $- \frac { 12 } { x - 3 }$ 
B)  0 
C)  $\frac { 12 } { x - 3 }$ 
D)  $\frac { 6 } { x - 3 }$ 
A)  $- \frac { 12 } { x - 3 }$ 
B)  0 
C)  $\frac { 12 } { x - 3 }$ 
D)  $\frac { 6 } { x - 3 }$

Question 5

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 2 x - 9 } { 2 x - 1 }$$

Accepted Answer

A)  cannot be simplified 
B)  9 
C)  $\frac { 2 } { x - 1 }$ 
D)  2 
A)  cannot be simplified 
B)  9 
C)  $\frac { 2 } { x - 1 }$ 
D)  2

Question 6

Provide an appropriate response.
-A tennis racket company has manufacturing costs given by the equation C = 30x + 30,000x where x is the number of rackets manufactured and C is the cost to manufacture each racket.
What number of rackets must be manufactured to bring the cost per racket to $3?

Accepted Answer

A)  No number of rackets manufactured satisfies this goal. 
B)  Not enough information is given to answer this question. 
C)  30,000 rackets 
D)  33,000 rackets 
A)  No number of rackets manufactured satisfies this goal. 
B)  Not enough information is given to answer this question. 
C)  30,000 rackets 
D)  33,000 rackets

Question 7

Multiply. Simplify if possible.
-$$\frac { 6 y } { 12 y + 6 } \cdot \frac { 14 y + 7 } { 6 }$$

Accepted Answer

A)  $\frac { 7 } { 6 }$ 
B)  $\frac { 7 y } { 36 }$ 
C)  $\frac { 7 y } { 6 }$ 
D)  $\frac { y } { 6 }$ 
A)  $\frac { 7 } { 6 }$ 
B)  $\frac { 7 y } { 36 }$ 
C)  $\frac { 7 y } { 6 }$ 
D)  $\frac { y } { 6 }$

Question 8

Perform the indicated operation. Simplify if possible.
-Express the perimeter of the triangle as a fully simplified rational expression.

Accepted Answer

A)  $\frac { 14 x + 42 } { 3 x + 9 } m$ 
B)  $14 \mathrm {~m}$ 
C)  $14 \mathrm { x } + 42 \mathrm {~m}$ 
D)  $\frac { 14 } { x + 3 } m$ 
A)  $\frac { 14 x + 42 } { 3 x + 9 } m$ 
B)  $14 \mathrm {~m}$ 
C)  $14 \mathrm { x } + 42 \mathrm {~m}$ 
D)  $\frac { 14 } { x + 3 } m$

Question 9

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { 8 } { x - 10 } - \frac { 3 } { 10 - x }$$

Accepted Answer

A)  $- \frac { 11 } { x - 10 }$ 
B)  $\frac { 5 } { 10 - x }$ 
C)  $- \frac { 5 } { x - 10 }$ 
D)  $\frac { 11 } { x - 10 }$ 
A)  $- \frac { 11 } { x - 10 }$ 
B)  $\frac { 5 } { 10 - x }$ 
C)  $- \frac { 5 } { x - 10 }$ 
D)  $\frac { 11 } { x - 10 }$

Question 10

Perform the indicated operation. Simplify if possible.
-$$\frac { x } { 13 } + \frac { 6 } { 13 }$$

Accepted Answer

A)  $\frac { 6 x } { 13 }$ 
B)  $\frac { x + 6 } { 13 }$ 
C)  $\frac { x + 6 } { 26 }$ 
D)  $\frac { 6 x } { 26 }$ 
A)  $\frac { 6 x } { 13 }$ 
B)  $\frac { x + 6 } { 13 }$ 
C)  $\frac { x + 6 } { 26 }$ 
D)  $\frac { 6 x } { 26 }$

Question 11

Provide an appropriate response.
-A snowboard company has manufacturing costs given by the equation $$C = \frac { \mathrm { Tx } + 1000 \mathrm {~T} } { \mathrm { x } }$$ where T is a different constant for each model, x is the number of snowboards manufactured, and C is the cost to manufacture one snowboard of a particular model. Choose which of the following statements are true with
Regard to this mathematical model.
I. The manufacturing cost per snowboard is the same for all models if 8000 of each model is manufactured.
II. The manufacturing cost per snowboard decreases for all models as the number manufactured increases.
III. The manufacturing cost per snowboard decreases for only some models as the number manufactured increases.

Accepted Answer

A)  Only II is true. 
B)  All three statements are true. 
C)  Only I and III are true. 
D)  Only I and II are true. 
A)  Only II is true. 
B)  All three statements are true. 
C)  Only I and III are true. 
D)  Only I and II are true.

Question 12

Multiply. Simplify if possible.
-$$\frac { \mathrm { k } ^ { 2 } + 6 \mathrm { k } + 9 } { \mathrm { k } ^ { 2 } + 10 \mathrm { k } + 21 } \cdot \frac { \mathrm { k } ^ { 2 } + 7 \mathrm { k } } { \mathrm { k } ^ { 2 } - 5 \mathrm { k } - 24 }$$

Accepted Answer

A)  $\frac { \mathrm { k } } { \mathrm { k } - 8 }$ 
B)  $\frac { k } { k ^ { 2 } + 10 k + 21 }$ 
C)  $\frac { \mathrm { k } ^ { 2 } + 7 \mathrm { k } } { \mathrm { k } - 8 }$ 
D)  $\frac { 1 } { \mathrm { k } - 8 }$ 
A)  $\frac { \mathrm { k } } { \mathrm { k } - 8 }$ 
B)  $\frac { k } { k ^ { 2 } + 10 k + 21 }$ 
C)  $\frac { \mathrm { k } ^ { 2 } + 7 \mathrm { k } } { \mathrm { k } - 8 }$ 
D)  $\frac { 1 } { \mathrm { k } - 8 }$

Question 13

Divide. Simplify if possible.
-$$\frac { 3 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 16 }$$

Accepted Answer

A)  $\frac { x } { 12 }$ 
B)  $\frac { 12 } { x }$ 
C)  $\frac { 48 x ^ { 2 } } { 4 x ^ { 3 } }$ 
D)  $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$ 
A)  $\frac { x } { 12 }$ 
B)  $\frac { 12 } { x }$ 
C)  $\frac { 48 x ^ { 2 } } { 4 x ^ { 3 } }$ 
D)  $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$

Question 14

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { x ^ { 2 } - x y + 9 x - 9 y } { x + 9 }$$

Accepted Answer

A)  $x - 2 y + 1$ 
B)  $\frac { 1 } { x + 9 }$ 
C)  cannot be simplified 
D)  $x - y$ 
A)  $x - 2 y + 1$ 
B)  $\frac { 1 } { x + 9 }$ 
C)  cannot be simplified 
D)  $x - y$

Question 15

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$\frac { 2 x + 3 } { 10 x ^ { 2 } + 21 x + 9 }$

Accepted Answer

A)  $\frac { 2 x } { 5 x + 3 }$ 
B)  $\frac { 1 } { 5 x + 3 }$ 
C)  $\frac { 2 x + 5 } { 5 x + 21 }$ 
D)  cannot be simplified 
A)  $\frac { 2 x } { 5 x + 3 }$ 
B)  $\frac { 1 } { 5 x + 3 }$ 
C)  $\frac { 2 x + 5 } { 5 x + 21 }$ 
D)  cannot be simplified

Question 16

Divide. Simplify if possible.
-$$\frac { 15 x ^ { 2 } - 37 x y + 20 y ^ { 2 } } { 35 x ^ { 2 } - 43 x y + 12 y ^ { 2 } } + \frac { 15 x ^ { 2 } - 31 x y + 10 y ^ { 2 } } { 30 x ^ { 2 } + 23 x y - 14 y ^ { 2 } }$$

Accepted Answer

A)  $\frac { ( 7 x + 3 y ) } { ( 6 x - 7 y ) }$ 
B)  $\frac { ( 3 x - 5 y ) ^ { 2 } } { ( 6 x + 7 y ) ( 7 x - 3 y ) }$ 
C)  $\frac { 6 x + 7 y } { 7 x - 3 y }$ 
D)  $\frac { ( 3 x + 5 y ) ^ { 2 } } { ( 6 x - 7 y ) ( 7 x + 3 y ) }$ 
A)  $\frac { ( 7 x + 3 y ) } { ( 6 x - 7 y ) }$ 
B)  $\frac { ( 3 x - 5 y ) ^ { 2 } } { ( 6 x + 7 y ) ( 7 x - 3 y ) }$ 
C)  $\frac { 6 x + 7 y } { 7 x - 3 y }$ 
D)  $\frac { ( 3 x + 5 y ) ^ { 2 } } { ( 6 x - 7 y ) ( 7 x + 3 y ) }$

Question 17

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { 5 } { x - 6 } - \frac { 3 } { 6 - x }$$

Accepted Answer

A)  $\frac { 2 } { 6 - x }$ 
B)  $\frac { 8 } { x - 6 }$ 
C)  $- \frac { 2 } { x - 6 }$ 
D)  $\frac { 2 } { x - 6 }$ 
A)  $\frac { 2 } { 6 - x }$ 
B)  $\frac { 8 } { x - 6 }$ 
C)  $- \frac { 2 } { x - 6 }$ 
D)  $\frac { 2 } { x - 6 }$

Question 18

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 7 x ^ { 2 } - 57 x + 8 } { x - 8 }$$

Accepted Answer

A)  $7 x ^ { 2 } - 58$ 
B)  $\frac { 1 } { x - 8 }$ 
C)  cannot be simplified 
D)  $7 x - 1$ 
A)  $7 x ^ { 2 } - 58$ 
B)  $\frac { 1 } { x - 8 }$ 
C)  cannot be simplified 
D)  $7 x - 1$

Question 19

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { x ^ { 2 } - 16 } { 4 - x }$$

Accepted Answer

A)  $- x + 4$ 
B)  $x - 4$ 
C)  $- x - 4$ 
D)  cannot be simplified 
A)  $- x + 4$ 
B)  $x - 4$ 
C)  $- x - 4$ 
D)  cannot be simplified

Question 20

Perform the indicated operation. Simplify if possible.
-Find the perimeter of the trapezoid.

Accepted Answer

A)  $\frac { x + 9 } { x + 3 }$ in. 
B)  $\frac { 4 x + 9 } { x + 3 }$ in. 
C)  $\frac { 2 x + 9 } { x + 3 }$ in. 
D)  $x + 6$ in. 
A)  $\frac { x + 9 } { x + 3 }$ in. 
B)  $\frac { 4 x + 9 } { x + 3 }$ in. 
C)  $\frac { 2 x + 9 } { x + 3 }$ in. 
D)  $x + 6$ in.

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x ^ { 2 } - 2 x + 6 x - 12 } { 2 x ^ { 2 } + 9 x + 12 x + 54 }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. -x² - 16 x² - 11x + 28

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { 6 } { a + 3 }$

Add or subtract as indicated. Simplify the result, if possible. - $\frac { 6 } { x - 3 } + \frac { 6 } { 3 - x }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 2 x - 9 } { 2 x - 1 }$

Provide an appropriate response. -A tennis racket company has manufacturing costs given by the equation C = 30x + 30,000x where x is the number of rackets manufactured and C is the cost to manufacture each racket. What number of rackets must be manufactured to bring the cost per racket to $3?

Multiply. Simplify if possible. - $\frac { 6 y } { 12 y + 6 } \cdot \frac { 14 y + 7 } { 6 }$

Perform the indicated operation. Simplify if possible. -Express the perimeter of the triangle as a fully simplified rational expression.

Add or subtract as indicated. Simplify the result, if possible. - $\frac { 8 } { x - 10 } - \frac { 3 } { 10 - x }$

Perform the indicated operation. Simplify if possible. - $\frac { x } { 13 } + \frac { 6 } { 13 }$

Multiply. Simplify if possible. - $\frac { \mathrm { k } ^ { 2 } + 6 \mathrm { k } + 9 } { \mathrm { k } ^ { 2 } + 10 \mathrm { k } + 21 } \cdot \frac { \mathrm { k } ^ { 2 } + 7 \mathrm { k } } { \mathrm { k } ^ { 2 } - 5 \mathrm { k } - 24 }$

Divide. Simplify if possible. - $\frac { 3 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 16 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x ^ { 2 } - x y + 9 x - 9 y } { x + 9 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 2 x + 3 } { 10 x ^ { 2 } + 21 x + 9 }$

Divide. Simplify if possible. - $\frac { 15 x ^ { 2 } - 37 x y + 20 y ^ { 2 } } { 35 x ^ { 2 } - 43 x y + 12 y ^ { 2 } } + \frac { 15 x ^ { 2 } - 31 x y + 10 y ^ { 2 } } { 30 x ^ { 2 } + 23 x y - 14 y ^ { 2 } }$

Add or subtract as indicated. Simplify the result, if possible. - $\frac { 5 } { x - 6 } - \frac { 3 } { 6 - x }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 7 x ^ { 2 } - 57 x + 8 } { x - 8 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x ^ { 2 } - 16 } { 4 - x }$

Perform the indicated operation. Simplify if possible. -Find the perimeter of the trapezoid.

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Basics of Functions

Inequalities and Problem Solving

Radicals, Radical Functions, and Rational Exponents

Filters

Exam 7: Rational Expressions

Simplify the rational expression. If the rational expression cannot be simplified, so state. - x2−2x+6x−122x2+9x+12x+54\frac { x ^ { 2 } - 2 x + 6 x - 12 } { 2 x ^ { 2 } + 9 x + 12 x + 54 }2x2+9x+12x+54x2−2x+6x−12​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. -x2 - 16 x2 - 11x + 28

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - 6a+3\frac { 6 } { a + 3 }a+36​

Add or subtract as indicated. Simplify the result, if possible. - 6x−3+63−x\frac { 6 } { x - 3 } + \frac { 6 } { 3 - x }x−36​+3−x6​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 2x−92x−1\frac { 2 x - 9 } { 2 x - 1 }2x−12x−9​