Question 1

Simplify the rational expression. (Assume the denominator is nonzero.)
-$\frac { 18 x ^ { 3 } } { 6 x }$

Accepted Answer

A)  $12 x ^ { 2 }$ 
B)  $3 x ^ { 2 }$ 
C)  12 
D)  $3 x$ 
A)  $12 x ^ { 2 }$ 
B)  $3 x ^ { 2 }$ 
C)  12 
D)  $3 x$

Question 2

Solve the problem.
-A contractor finds that it takes Julie 9 hours to construct a wall of a certain size. It takes Leann 7 hours to construct the same wall. How long would it take if they worked together?

Accepted Answer

A)  $\frac { 16 } { 63 }$ hours 
B)  1 hour 
C)  $3 \frac { 15 } { 16 }$ hours 
D)  16 hours 
A)  $\frac { 16 } { 63 }$ hours 
B)  1 hour 
C)  $3 \frac { 15 } { 16 }$ hours 
D)  16 hours

Question 3

Subtract.
-$$\frac { 3 x + 12 } { x ^ { 2 } - 3 x - 18 } - \frac { x + 6 } { x ^ { 2 } - 3 x - 18 }$$

Accepted Answer

A)  $\frac { 2 x + 18 } { x ^ { 2 } - 3 x - 18 }$ 
B)  $2 x + 6$ 
C)  $\frac { 1 } { x - 3 }$ 
D)  $\frac { 2 } { x - 6 }$ 
A)  $\frac { 2 x + 18 } { x ^ { 2 } - 3 x - 18 }$ 
B)  $2 x + 6$ 
C)  $\frac { 1 } { x - 3 }$ 
D)  $\frac { 2 } { x - 6 }$

Question 4

Find the domain of the rational function.
-$$r ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 13 x + 36 }$$

Accepted Answer

A)  All real numbers except $- 9$ and $- 4$. 
B)  All real numbers except 9 and 4 . 
C)  All real numbers except $- 4$ and 9 . 
D)  All real numbers except $- 9$ and 4 
A)  All real numbers except $- 9$ and $- 4$. 
B)  All real numbers except 9 and 4 . 
C)  All real numbers except $- 4$ and 9 . 
D)  All real numbers except $- 9$ and 4

Question 5

Subtract.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) }$ 
B)  $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
C)  $\frac { x ^ { 2 } - 5 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
D)  $\frac { x ^ { 2 } + 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
A)  $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) }$ 
B)  $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
C)  $\frac { x ^ { 2 } - 5 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
D)  $\frac { x ^ { 2 } + 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

Question 6

Solve the problem.
-One maid can clean the house in 3 hours. Another maid can do the job in 6 hours. How long will it take them to do the job working together?

Accepted Answer

A)  $\frac { 1 } { 18 }$ hours 
B)  $\frac { 1 } { 9 }$ hours 
C)  6 hours 
D)  2 hours 
A)  $\frac { 1 } { 18 }$ hours 
B)  $\frac { 1 } { 9 }$ hours 
C)  6 hours 
D)  2 hours

Question 7

Simplify the complex fraction.
-$\frac { \frac { 1 } { 7 } - \frac { 1 } { x } } { \frac { 7 - x } { 7 } }$

Accepted Answer

A)  $- \frac { 7 } { x }$ 
B)  $- x$ 
C)  $- \frac { 1 } { x }$ 
D)  $\frac { 1 } { x }$ 
A)  $- \frac { 7 } { x }$ 
B)  $- x$ 
C)  $- \frac { 1 } { x }$ 
D)  $\frac { 1 } { x }$

Question 8

Add.
-$$\frac { x } { x - 6 } + \frac { 1 } { x - 6 }$$

Accepted Answer

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

Question 9

Find the missing numerator.
-$\frac { x ^ { 2 } - 10 x } { x - 6 } + \frac { ? } { x - 6 } = x - 4$

Accepted Answer

A)  $x - 6$ 
B)  $x + 6$ 
C)  4 
D)  24 
A)  $x - 6$ 
B)  $x + 6$ 
C)  4 
D)  24

Question 10

Evaluate the rational expression for the given value of the variable
-$\frac { x ^ { 2 } + 7 x + 5 } { x ^ { 2 } + 2 x - 10 }$ for $x = 2$

Accepted Answer

A)  $= \frac { 21 } { 4 }$ 
B)  $- \frac { 3 } { 2 }$ 
C)  $- 4$ 
D)  $-\frac { 23 } { 2 }$ 
A)  $= \frac { 21 } { 4 }$ 
B)  $- \frac { 3 } { 2 }$ 
C)  $- 4$ 
D)  $-\frac { 23 } { 2 }$

Question 11

Evaluate the rational function.
-$$r ( x ) = \frac { x ^ { 3 } + 3 x ^ { 2 } - 15 x + 7 } { x ^ { 2 } + 6 x - 14 } , r ( - 3 )$$

Accepted Answer

A)  $\frac { 26 } { 23 }$ 
B)  $\frac { 52 } { 23 }$ 
C)  $- \frac { 52 } { 23 }$ 
D)  Undefined 
A)  $\frac { 26 } { 23 }$ 
B)  $\frac { 52 } { 23 }$ 
C)  $- \frac { 52 } { 23 }$ 
D)  Undefined

Question 12

Solve.
-One number is one larger than another positive number. If the reciprocal of the smaller number is multiplied by the reciprocal of the larger number, the product is $\frac { 1 } { 182 }$. Find the two numbers.

Accepted Answer

A)  14,15 
B)  13,14 
C)  12,13 
D)  11,12 
A)  14,15 
B)  13,14 
C)  12,13 
D)  11,12

Question 13

Subtract.
-$$\frac { x + 13 } { 8 x } - \frac { x - 10 } { 3 x }$$

Accepted Answer

A)  $\frac { - 5 x + 119 } { 8 x }$ 
B)  $\frac { - 5 x + 119 } { 24 }$ 
C)  $\frac { - 5 x + 119 } { 24 x }$ 
D)  $\frac { - 5 x + 119 } { x }$ 
A)  $\frac { - 5 x + 119 } { 8 x }$ 
B)  $\frac { - 5 x + 119 } { 24 }$ 
C)  $\frac { - 5 x + 119 } { 24 x }$ 
D)  $\frac { - 5 x + 119 } { x }$

Question 14

Add.
-$$\frac { x ^ { 2 } - 7 x - 55 } { x ^ { 2 } + 2 x - 15 } + \frac { x ^ { 2 } + 5 x - 5 } { x ^ { 2 } + 2 x - 15 }$$

Accepted Answer

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

Question 15

Add or subtract.
-$\frac { 7 - x } { x - 4 } - \frac { 2 x - 4 } { 4 - x }$

Accepted Answer

A)  $\frac { x + 11 } { x - 4 }$ 
B)  $\frac { x + 3 } { x - 4 }$ 
C)  $- \frac { x + 11 } { x - 4 }$ 
D)  $- \frac { x + 3 } { x - 4 }$ 
A)  $\frac { x + 11 } { x - 4 }$ 
B)  $\frac { x + 3 } { x - 4 }$ 
C)  $- \frac { x + 11 } { x - 4 }$ 
D)  $- \frac { x + 3 } { x - 4 }$

Question 16

Subtract.
-$\frac { 2 } { 21 x } - \frac { 4 } { 15 x ^ { 2 } }$

Accepted Answer

A)  $- \frac { 2 } { 315 x ^ { 2 } }$ 
B)  $\frac { 2 ( 5 x - 14 ) } { 105 x ^ { 2 } }$ 
C)  $\frac { 2 } { 21 x + 15 x ^ { 2 } }$ 
D)  $\frac { 10 x - 28 } { 105 x ^ { 2 } }$ 
A)  $- \frac { 2 } { 315 x ^ { 2 } }$ 
B)  $\frac { 2 ( 5 x - 14 ) } { 105 x ^ { 2 } }$ 
C)  $\frac { 2 } { 21 x + 15 x ^ { 2 } }$ 
D)  $\frac { 10 x - 28 } { 105 x ^ { 2 } }$

Question 17

Add.
-$$\frac { 5 } { x + 5 } + \frac { 3 } { x }$$

Accepted Answer

A)  $\frac { 5 x + 15 } { x ( x + 5 ) }$ 
B)  $\frac { 8 x + 15 } { ( x + 5 ) }$ 
C)  $\frac { 8 x + 15 } { x ( x + 5 ) }$ 
D)  $\frac { 8 x + 15 } { x }$ 
A)  $\frac { 5 x + 15 } { x ( x + 5 ) }$ 
B)  $\frac { 8 x + 15 } { ( x + 5 ) }$ 
C)  $\frac { 8 x + 15 } { x ( x + 5 ) }$ 
D)  $\frac { 8 x + 15 } { x }$

Question 18

Find the missing numerator and denominator.
-$$\frac { 7 x ^ { 2 } - 28 x } { x ^ { 2 } - 6 x - 40 } \div \frac { ? } { ? } = \frac { 7 x } { x - 10 }$$

Accepted Answer

A)  $\frac { x - 10 } { 7 x }$ 
B)  $\frac { x + 10 } { 7 x }$ 
C)  $\frac { x - 4 } { x + 4 }$ 
D)  $\frac { 7 x } { x + 10 }$ 
A)  $\frac { x - 10 } { 7 x }$ 
B)  $\frac { x + 10 } { 7 x }$ 
C)  $\frac { x - 4 } { x + 4 }$ 
D)  $\frac { 7 x } { x + 10 }$

Question 19

Divide.
-$$\frac { x ^ { 2 } - 9 } { 25 x ^ { 2 } - 4 } \div \frac { x - 3 } { 2 - 5 x }$$

Accepted Answer

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

Question 20

For the given rational functions f(x) and g(x), f(x) -g(x).
-$$f ( x ) = \frac { 2 } { x - 8 } , g ( x ) = \frac { 19 } { x - 8 }$$

Accepted Answer

A)  $- \frac { 17 } { x }$ 
B)  $\frac { 17 } { x - 8 }$ 
C)  $\frac { 21 } { x - 8 }$ 
D)  $- \frac { 17 } { x - 8 }$ 
A)  $- \frac { 17 } { x }$ 
B)  $\frac { 17 } { x - 8 }$ 
C)  $\frac { 21 } { x - 8 }$ 
D)  $- \frac { 17 } { x - 8 }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { 18 x ^ { 3 } } { 6 x }$

Solve the problem. -A contractor finds that it takes Julie 9 hours to construct a wall of a certain size. It takes Leann 7 hours to construct the same wall. How long would it take if they worked together?

Subtract. - $\frac { 3 x + 12 } { x ^ { 2 } - 3 x - 18 } - \frac { x + 6 } { x ^ { 2 } - 3 x - 18 }$

Find the domain of the rational function. - $r ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 13 x + 36 }$

Subtract. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }$

Solve the problem. -One maid can clean the house in 3 hours. Another maid can do the job in 6 hours. How long will it take them to do the job working together?

Simplify the complex fraction. - $\frac { \frac { 1 } { 7 } - \frac { 1 } { x } } { \frac { 7 - x } { 7 } }$

Add. - $\frac { x } { x - 6 } + \frac { 1 } { x - 6 }$

Find the missing numerator. - $\frac { x ^ { 2 } - 10 x } { x - 6 } + \frac { ? } { x - 6 } = x - 4$

Evaluate the rational expression for the given value of the variable - $\frac { x ^ { 2 } + 7 x + 5 } { x ^ { 2 } + 2 x - 10 }$ for $x = 2$

Evaluate the rational function. - $r ( x ) = \frac { x ^ { 3 } + 3 x ^ { 2 } - 15 x + 7 } { x ^ { 2 } + 6 x - 14 } , r ( - 3 )$

Solve. -One number is one larger than another positive number. If the reciprocal of the smaller number is multiplied by the reciprocal of the larger number, the product is $\frac { 1 } { 182 }$ . Find the two numbers.

Subtract. - $\frac { x + 13 } { 8 x } - \frac { x - 10 } { 3 x }$

Add. - $\frac { x ^ { 2 } - 7 x - 55 } { x ^ { 2 } + 2 x - 15 } + \frac { x ^ { 2 } + 5 x - 5 } { x ^ { 2 } + 2 x - 15 }$

Add or subtract. - $\frac { 7 - x } { x - 4 } - \frac { 2 x - 4 } { 4 - x }$

Subtract. - $\frac { 2 } { 21 x } - \frac { 4 } { 15 x ^ { 2 } }$

Add. - $\frac { 5 } { x + 5 } + \frac { 3 } { x }$

Find the missing numerator and denominator. - $\frac { 7 x ^ { 2 } - 28 x } { x ^ { 2 } - 6 x - 40 } \div \frac { ? } { ? } = \frac { 7 x } { x - 10 }$

Divide. - $\frac { x ^ { 2 } - 9 } { 25 x ^ { 2 } - 4 } \div \frac { x - 3 } { 2 - 5 x }$

For the given rational functions f(x) and g(x), f(x) -g(x). - $f ( x ) = \frac { 2 } { x - 8 } , g ( x ) = \frac { 19 } { x - 8 }$

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

Simplify the rational expression. (Assume the denominator is nonzero.) - 18x36x\frac { 18 x ^ { 3 } } { 6 x }6x18x3​

Solve the problem. -A contractor finds that it takes Julie 9 hours to construct a wall of a certain size. It takes Leann 7 hours to construct the same wall. How long would it take if they worked together?

Subtract. - 3x+12x2−3x−18−x+6x2−3x−18\frac { 3 x + 12 } { x ^ { 2 } - 3 x - 18 } - \frac { x + 6 } { x ^ { 2 } - 3 x - 18 }x2−3x−183x+12​−x2−3x−18x+6​

Find the domain of the rational function. - r(x)=x2+x−9x2−13x+36r ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 13 x + 36 }r(x)=x2−13x+36x2+x−9​

Subtract. - xx2−16−6x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+46​