Question 1

Determine whether the two binomials are or are not opposites.
-x + 7 and 7 + x

Accepted Answer

A)  Opposites 
B)  Not opposites 
A)  Opposites 
B)  Not opposites

Question 2

Solve the problem.
-The speed of a stream is 6 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream, what is the speed of the boat in still water?

Accepted Answer

A)  18 mph 
B)  21 mph 
C)  12 mph 
D)  20 mph 
A)  18 mph 
B)  21 mph 
C)  12 mph 
D)  20 mph

Question 3

Add.
-$$\frac { 7 x } { x + 5 } + \frac { 2 } { x - 5 }$$

Accepted Answer

A)  $\frac { 7 x ^ { 2 } - 33 x + 10 } { x ^ { 2 } - 25 }$ 
B)  $\frac { 7 x ^ { 2 } - 33 x + 10 } { x ^ { 2 } + 10 x + 25 }$ 
C)  $\frac { 7 x + 2 } { ( x + 5 ) ( x - 5 ) }$ 
D)  $\frac { 7 x ^ { 2 } - 33 x + 10 } { x ^ { 2 } - 10 x + 25 }$ 
A)  $\frac { 7 x ^ { 2 } - 33 x + 10 } { x ^ { 2 } - 25 }$ 
B)  $\frac { 7 x ^ { 2 } - 33 x + 10 } { x ^ { 2 } + 10 x + 25 }$ 
C)  $\frac { 7 x + 2 } { ( x + 5 ) ( x - 5 ) }$ 
D)  $\frac { 7 x ^ { 2 } - 33 x + 10 } { x ^ { 2 } - 10 x + 25 }$

Question 4

Identify the given function as a linear function, a quadratic function, or a rational function.
-$$f ( x ) = 7 x + 8$$

Accepted Answer

A)  Rational 
B)  Linear 
C)  Quadratic 
A)  Rational 
B)  Linear 
C)  Quadratic

Question 5

Find the LCD of the given rational expressions.
-$$\frac { 8 } { 9 x + 36 } , \frac { 3 } { x ^ { 2 } + 4 x }$$

Accepted Answer

A)  $9 x ( x + 4 )$ 
B)  $9 x + 4$ 
C)  $9 x ^ { 2 } + 36$ 
D)  $9 x ^ { 2 } + 4$ 
A)  $9 x ( x + 4 )$ 
B)  $9 x + 4$ 
C)  $9 x ^ { 2 } + 36$ 
D)  $9 x ^ { 2 } + 4$

Question 6

Solve.
-The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of
5 miles?

Accepted Answer

A)  1306 units 
B)  1244 units 
C)  1280 units 
D)  1263 units 
A)  1306 units 
B)  1244 units 
C)  1280 units 
D)  1263 units

Question 7

Find all values of the variable for which the rational expression is undefined.
-$$\frac { x - 6 } { 6 x - 24 }$$

Accepted Answer

A)  0 
B)  4 
C)  $- 6$ 
D)  24 
A)  0 
B)  4 
C)  $- 6$ 
D)  24

Question 8

Add.
-$$\frac { 3 } { ( x + 6 ) ^ { 2 } } + \frac { 2 } { x + 6 }$$

Accepted Answer

A)  $\frac { 3 x + 20 } { ( x + 6 ) ^ { 2 } }$ 
B)  $\frac { 2 x + 15 } { ( x + 6 ) ^ { 2 } }$ 
C)  $\frac { 5 } { x + 6 }$ 
D)  $\frac { 2 x + 5 } { ( x + 6 ) ^ { 2 } }$ 
A)  $\frac { 3 x + 20 } { ( x + 6 ) ^ { 2 } }$ 
B)  $\frac { 2 x + 15 } { ( x + 6 ) ^ { 2 } }$ 
C)  $\frac { 5 } { x + 6 }$ 
D)  $\frac { 2 x + 5 } { ( x + 6 ) ^ { 2 } }$

Question 9

Find all values of the variable for which the rational expression is undefined.
-$\frac { 36 x } { x ^ { 2 } - 4 x - 12 }$

Accepted Answer

A)  0 
B)  $- 6,2$ 
C)  $- 6,6$ 
D)  $- 2,6$ 
A)  0 
B)  $- 6,2$ 
C)  $- 6,6$ 
D)  $- 2,6$

Question 10

Solve.
-y varies inversely as x. If y = 48 when x = 9 $\text { find } y \text { when } x$

Accepted Answer

A)  27 
B)  54 
C)  9 
D)  $\frac { 128 } { 3 }$ 
A)  27 
B)  54 
C)  9 
D)  $\frac { 128 } { 3 }$

Question 11

Find the LCD of the given rational expressions.
-$$\frac { 7 } { x ^ { 2 } + 7 x + 10 } , \frac { 5 } { x ^ { 2 } + 6 x + 5 }$$

Accepted Answer

A)  $( x + 2 ) ( x + 5 )$ 
B)  $( x + 5 ) ( x + 1 )$ 
C)  $( x + 2 ) ( x + 5 ) ( x + 1 )$ 
D)  $( x - 2 ) ( x - 5 ) ( x + 1 )$ 
A)  $( x + 2 ) ( x + 5 )$ 
B)  $( x + 5 ) ( x + 1 )$ 
C)  $( x + 2 ) ( x + 5 ) ( x + 1 )$ 
D)  $( x - 2 ) ( x - 5 ) ( x + 1 )$

Question 12

Solve.
-varies directly as $x$. If $y = \frac { 17 } { 2 }$ when $x = 17$, find $y$ when $x = 6$.

Accepted Answer

A)  $\frac { 17 } { 6 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  3 
D)  $\frac { 289 } { 12 }$ 
A)  $\frac { 17 } { 6 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  3 
D)  $\frac { 289 } { 12 }$

Question 13

Subtract.
-$$\frac { 5 x } { x - 2 } - \frac { 10 } { x - 2 }$$

Accepted Answer

A)  $\frac { 5 } { x - 2 }$ 
B)  $\frac { 5 ( x + 2 ) } { x - 2 }$ 
C)  5 
D)  0 
A)  $\frac { 5 } { x - 2 }$ 
B)  $\frac { 5 ( x + 2 ) } { x - 2 }$ 
C)  5 
D)  0

Determine whether the two binomials are or are not opposites. -x + 7 and 7 + x

Solve the problem. -The speed of a stream is 6 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream, what is the speed of the boat in still water?

Add. - $\frac { 7 x } { x + 5 } + \frac { 2 } { x - 5 }$

Identify the given function as a linear function, a quadratic function, or a rational function. - $f ( x ) = 7 x + 8$

Find the LCD of the given rational expressions. - $\frac { 8 } { 9 x + 36 } , \frac { 3 } { x ^ { 2 } + 4 x }$

Solve. -The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of 5 miles?

Find all values of the variable for which the rational expression is undefined. - $\frac { x - 6 } { 6 x - 24 }$

Add. - $\frac { 3 } { ( x + 6 ) ^ { 2 } } + \frac { 2 } { x + 6 }$

Find all values of the variable for which the rational expression is undefined. - $\frac { 36 x } { x ^ { 2 } - 4 x - 12 }$

Solve. -y varies inversely as x. If y = 48 when x = 9 $\text { find } y \text { when } x$

Find the LCD of the given rational expressions. - $\frac { 7 } { x ^ { 2 } + 7 x + 10 } , \frac { 5 } { x ^ { 2 } + 6 x + 5 }$

Solve. -varies directly as $x$ . If $y = \frac { 17 } { 2 }$ when $x = 17$ , find $y$ when $x = 6$ .

Subtract. - $\frac { 5 x } { x - 2 } - \frac { 10 } { x - 2 }$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Rational Expressions and Equations