Question 1

Solve.
-The sum of a number and its reciprocal is -2. Find the number.

Accepted Answer

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

Question 2

Evaluate the rational expression for the given value of the variable
-$\frac { x } { x - 9 }$ for $x = - 9$

Accepted Answer

A)  $- \frac { 1 } { 9 }$ 
B)  Undefined 
C)  0 
D)  $\frac { 1 } { 2 }$ 
A)  $- \frac { 1 } { 9 }$ 
B)  Undefined 
C)  0 
D)  $\frac { 1 } { 2 }$

Question 3

Subtract.
-$$\frac { 2 x ^ { 2 } + 20 } { x ^ { 2 } + 5 x - 6 } - \frac { 13 x } { x ^ { 2 } + 5 x - 6 }$$

Accepted Answer

A)  $\frac { ( x - 4 ) ( 2 x - 5 ) } { ( x + 6 ) ( x - 1 ) }$ 
B)  $\frac { ( x - 4 ) ( 2 x + 5 ) } { ( x + 6 ) ( x - 1 ) }$ 
C)  $\frac { ( x + 4 ) ( 2 x + 5 ) } { ( x + 6 ) ( x - 1 ) }$ 
D)  $\frac { 2 x - 5 } { x - 1 }$ 
A)  $\frac { ( x - 4 ) ( 2 x - 5 ) } { ( x + 6 ) ( x - 1 ) }$ 
B)  $\frac { ( x - 4 ) ( 2 x + 5 ) } { ( x + 6 ) ( x - 1 ) }$ 
C)  $\frac { ( x + 4 ) ( 2 x + 5 ) } { ( x + 6 ) ( x - 1 ) }$ 
D)  $\frac { 2 x - 5 } { x - 1 }$

Question 4

Evaluate the rational function.
-$$r ( x ) = \frac { 17 } { x ^ { 2 } - 9 x + 20 } , r ( - 8 )$$

Accepted Answer

A)  Undefined 
B)  $\frac { 17 } { 156 }$ 
C)  $\frac { 1 } { 78 }$ 
D)  $- \frac { 17 } { 156 }$ 
A)  Undefined 
B)  $\frac { 17 } { 156 }$ 
C)  $\frac { 1 } { 78 }$ 
D)  $- \frac { 17 } { 156 }$

Question 5

Solve the problem.
-Tom Quig traveled 300 miles east of St. Louis. For most of the trip he averaged 70 mph, but for one period of time he was slowed to 10 mph due to a major accident. If the total travel time was 6
Hours, for how many miles did he drive at the reduced speed?

Accepted Answer

A)  30 miles 
B)  40 miles 
C)  15 miles 
D)  20 miles 
A)  30 miles 
B)  40 miles 
C)  15 miles 
D)  20 miles

Question 6

Simplify the complex fraction.
-$\mathrm { S } = \frac { \mathrm { H } } { \mathrm { mt } 1 - \mathrm { mt } 2 }$ for $\mathrm { m }$

Accepted Answer

A)  $m = \frac { H } { S \left( t _ { 1 } - t _ { 2 } \right) }$ 
B)  $\mathrm { m } = \frac { \mathrm { H } } { \mathrm { St } _ { 1 } - \mathrm { t } _ { 2 } }$ 
C)  $m = \frac { S H } { t _ { 1 } - t _ { 2 } }$ 
D)  $\mathrm { m } = \frac { \mathrm { H } + \mathrm { St } _ { 2 } } { \mathrm { St } _ { 1 } }$ 
A)  $m = \frac { H } { S \left( t _ { 1 } - t _ { 2 } \right) }$ 
B)  $\mathrm { m } = \frac { \mathrm { H } } { \mathrm { St } _ { 1 } - \mathrm { t } _ { 2 } }$ 
C)  $m = \frac { S H } { t _ { 1 } - t _ { 2 } }$ 
D)  $\mathrm { m } = \frac { \mathrm { H } + \mathrm { St } _ { 2 } } { \mathrm { St } _ { 1 } }$

Question 7

Find the missing numerator and denominator.
-$$\frac { x ^ { 2 } - 8 x + 16 } { x ^ { 2 } - 49 } \cdot \frac { ? } { ? } = \frac { x - 4 } { x - 7 }$$

Accepted Answer

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

Question 8

Find the LCD of the given rational expressions.
-$$\frac { 3 } { x ^ { 2 } + 11 x + 30 } , \frac { 4 } { 2 x + 10 }$$

Accepted Answer

A)  $2 ( x + 6 ) ( x + 5 )$ 
B)  $2 ( x + 6 ) ( x - 5 )$ 
C)  $2 ( x - 6 ) ( x + 5 )$ 
D)  $2 ( x - 6 ) ( x - 5 )$ 
A)  $2 ( x + 6 ) ( x + 5 )$ 
B)  $2 ( x + 6 ) ( x - 5 )$ 
C)  $2 ( x - 6 ) ( x + 5 )$ 
D)  $2 ( x - 6 ) ( x - 5 )$

Question 9

Solve the problem.
-A boat can go 105 mph in still water. It takes as long to go 560 miles upstream as it does to go downstream 640 miles. How fast is the current?

Accepted Answer

A)  6 mph 
B)  1 mph 
C)  7 mph 
D)  8 mph 
A)  6 mph 
B)  1 mph 
C)  7 mph 
D)  8 mph

Question 10

Solve.
-$y$ varies inversely as $x$. If $y = \frac { 7 } { 2 }$ when $x = 9$, find $y$ when $x = 10$.

Accepted Answer

A)  $\frac { 81 } { 50 }$ 
B)  5 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 81 } { 20 }$ 
A)  $\frac { 81 } { 50 }$ 
B)  5 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 81 } { 20 }$

Question 11

Add.
-$$\frac { x ^ { 2 } - 8 x } { x - 2 } + \frac { 12 } { x - 2 }$$

Accepted Answer

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

Question 12

Add.
-$$\frac { 3 } { x } + \frac { 8 } { x - 9 }$$

Accepted Answer

A)  $\frac { 11 x - 27 } { x ( x - 9 ) }$ 
B)  $\frac { 11 x - 27 } { x ( 9 - x ) }$ 
C)  $\frac { 27 x - 11 } { x ( 9 - x ) }$ 
D)  $\frac { 27 x - 11 } { x ( x - 9 ) }$ 
A)  $\frac { 11 x - 27 } { x ( x - 9 ) }$ 
B)  $\frac { 11 x - 27 } { x ( 9 - x ) }$ 
C)  $\frac { 27 x - 11 } { x ( 9 - x ) }$ 
D)  $\frac { 27 x - 11 } { x ( x - 9 ) }$

Question 13

Find the missing numerator.
-$\frac { 9 x ^ { 2 } } { x - 1 } - \frac { ? } { x - 1 } = 9 x$

Accepted Answer

A)  $9 x$ 
B)  9 
C)  $\frac { 9 x ( x + 1 ) } { x - 1 }$ 
D)  $\frac { 9 x } { x - 1 }$ 
A)  $9 x$ 
B)  9 
C)  $\frac { 9 x ( x + 1 ) } { x - 1 }$ 
D)  $\frac { 9 x } { x - 1 }$

Question 14

Divide.
-$$\frac { x ^ { 2 } + 10 x + 21 } { x ^ { 2 } + 12 x + 27 } \div \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 5 x - 36 }$$

Accepted Answer

A)  $\frac { x - 4 } { x }$ 
B)  $x - 4$ 
C)  $\frac { x } { x ^ { 2 } + 12 x + 27 }$ 
D)  $\frac { x - 4 } { x ^ { 2 } + 9 x }$ 
A)  $\frac { x - 4 } { x }$ 
B)  $x - 4$ 
C)  $\frac { x } { x ^ { 2 } + 12 x + 27 }$ 
D)  $\frac { x - 4 } { x ^ { 2 } + 9 x }$

Question 15

For the given rational functions f(x) and g(x), f(x) -g(x).
-$$f ( x ) = \frac { 15 } { x - 3 } , g ( x ) = \frac { 5 x } { x - 3 }$$

Accepted Answer

A)  $- \frac { 5 } { x - 3 }$ 
B)  $- 5$ 
C)  $\frac { 5 } { x - 3 }$ 
D)  5 
A)  $- \frac { 5 } { x - 3 }$ 
B)  $- 5$ 
C)  $\frac { 5 } { x - 3 }$ 
D)  5

Question 16

Simplify the complex fraction.
-$\frac { 1 } { a } + \frac { 1 } { b } = \frac { 1 } { c }$ for $c$

Accepted Answer

A)  $c = \frac { a + b } { a b }$ 
B)  $c = a + b$ 
C)  $c = a b ( a + b )$ 
D)  $c = \frac { a b } { a + b }$ 
A)  $c = \frac { a + b } { a b }$ 
B)  $c = a + b$ 
C)  $c = a b ( a + b )$ 
D)  $c = \frac { a b } { a + b }$

Question 17

Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { x ^ { 2 } - 25 } { ( x + 5 ) ^ { 2 } }$$

Accepted Answer

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

Question 18

Subtract.
-$\frac { 7 x ^ { 2 } - 9 x + 8 } { x ^ { 2 } + 10 x + 21 } - \frac { 6 x ^ { 2 } - 9 x + 57 } { x ^ { 2 } + 10 x + 21 }$

Accepted Answer

A)  $\frac { x ^ { 2 } - 49 } { ( x + 3 ) ( x - 7 ) }$ 
B)  $\frac { 13 x ^ { 2 } - 18 x + 65 } { ( x + 3 ) ( x + 7 ) }$ 
C)  $\frac { x + 7 } { x + 3 }$ 
D)  $\frac { x - 7 } { x + 3 }$ 
A)  $\frac { x ^ { 2 } - 49 } { ( x + 3 ) ( x - 7 ) }$ 
B)  $\frac { 13 x ^ { 2 } - 18 x + 65 } { ( x + 3 ) ( x + 7 ) }$ 
C)  $\frac { x + 7 } { x + 3 }$ 
D)  $\frac { x - 7 } { x + 3 }$

Question 19

Solve the problem.
-One printer can do a printing job in 11 hours. Another printer can do the same job in 14 hours. How long can they do the job working together?

Accepted Answer

A)  $5 \frac { 12 } { 13 }$ hours 
B)  $\frac { 1 } { 25 }$ hours 
C)  $51 \frac { 1 } { 3 }$ hours 
D)  $6 \frac { 4 } { 25 }$ hours 
A)  $5 \frac { 12 } { 13 }$ hours 
B)  $\frac { 1 } { 25 }$ hours 
C)  $51 \frac { 1 } { 3 }$ hours 
D)  $6 \frac { 4 } { 25 }$ hours

Question 20

Identify the given function as a linear function, a quadratic function, or a rational function.
-$$f ( x ) = \frac { x ^ { 2 } } { x ^ { 3 } - 3 x - 10 }$$

Accepted Answer

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

Solve. -The sum of a number and its reciprocal is -2. Find the number.

Evaluate the rational expression for the given value of the variable - $\frac { x } { x - 9 }$ for $x = - 9$

Subtract. - $\frac { 2 x ^ { 2 } + 20 } { x ^ { 2 } + 5 x - 6 } - \frac { 13 x } { x ^ { 2 } + 5 x - 6 }$

Evaluate the rational function. - $r ( x ) = \frac { 17 } { x ^ { 2 } - 9 x + 20 } , r ( - 8 )$

Solve the problem. -Tom Quig traveled 300 miles east of St. Louis. For most of the trip he averaged 70 mph, but for one period of time he was slowed to 10 mph due to a major accident. If the total travel time was 6 Hours, for how many miles did he drive at the reduced speed?

Simplify the complex fraction. - $\mathrm { S } = \frac { \mathrm { H } } { \mathrm { mt } 1 - \mathrm { mt } 2 }$ for $\mathrm { m }$

Find the missing numerator and denominator. - $\frac { x ^ { 2 } - 8 x + 16 } { x ^ { 2 } - 49 } \cdot \frac { ? } { ? } = \frac { x - 4 } { x - 7 }$

Find the LCD of the given rational expressions. - $\frac { 3 } { x ^ { 2 } + 11 x + 30 } , \frac { 4 } { 2 x + 10 }$

Solve the problem. -A boat can go 105 mph in still water. It takes as long to go 560 miles upstream as it does to go downstream 640 miles. How fast is the current?

Solve. - $y$ varies inversely as $x$ . If $y = \frac { 7 } { 2 }$ when $x = 9$ , find $y$ when $x = 10$ .

Add. - $\frac { x ^ { 2 } - 8 x } { x - 2 } + \frac { 12 } { x - 2 }$

Add. - $\frac { 3 } { x } + \frac { 8 } { x - 9 }$

Find the missing numerator. - $\frac { 9 x ^ { 2 } } { x - 1 } - \frac { ? } { x - 1 } = 9 x$

Divide. - $\frac { x ^ { 2 } + 10 x + 21 } { x ^ { 2 } + 12 x + 27 } \div \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 5 x - 36 }$

For the given rational functions f(x) and g(x), f(x) -g(x). - $f ( x ) = \frac { 15 } { x - 3 } , g ( x ) = \frac { 5 x } { x - 3 }$

Simplify the complex fraction. - $\frac { 1 } { a } + \frac { 1 } { b } = \frac { 1 } { c }$ for $c$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { x ^ { 2 } - 25 } { ( x + 5 ) ^ { 2 } }$

Subtract. - $\frac { 7 x ^ { 2 } - 9 x + 8 } { x ^ { 2 } + 10 x + 21 } - \frac { 6 x ^ { 2 } - 9 x + 57 } { x ^ { 2 } + 10 x + 21 }$

Solve the problem. -One printer can do a printing job in 11 hours. Another printer can do the same job in 14 hours. How long can they do the job working together?

Identify the given function as a linear function, a quadratic function, or a rational function. - $f ( x ) = \frac { x ^ { 2 } } { x ^ { 3 } - 3 x - 10 }$

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

Solve. -The sum of a number and its reciprocal is -2. Find the number.

Evaluate the rational expression for the given value of the variable - xx−9\frac { x } { x - 9 }x−9x​ for x=−9x = - 9x=−9

Subtract. - 2x2+20x2+5x−6−13xx2+5x−6\frac { 2 x ^ { 2 } + 20 } { x ^ { 2 } + 5 x - 6 } - \frac { 13 x } { x ^ { 2 } + 5 x - 6 }x2+5x−62x2+20​−x2+5x−613x​

Evaluate the rational function. - r(x)=17x2−9x+20,r(−8)r ( x ) = \frac { 17 } { x ^ { 2 } - 9 x + 20 } , r ( - 8 )r(x)=x2−9x+2017​,r(−8)