Question 1

Evaluate the rational expression for the given value of the variable
-$\frac { x ^ { 2 } - 4 x } { x - 3 }$ for $x = 8$

Accepted Answer

A)  $\frac { 32 } { 5 }$ 
B)  0 
C)  Undefined 
D)  $- \frac { 32 } { 5 }$ 
A)  $\frac { 32 } { 5 }$ 
B)  0 
C)  Undefined 
D)  $- \frac { 32 } { 5 }$

Question 2

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

Accepted Answer

A)  8 
B)  54 
C)  6 
D)  81 
A)  8 
B)  54 
C)  6 
D)  81

Question 3

For the given functions f(x) and g(x), find f(x) ∙ g(x).
-$f ( x ) = \frac { 6 } { ( x - 6 ) } , g ( x ) = \frac { x ^ { 2 } - 3 x - 18 } { ( x + 3 ) ^ { 2 } }$

Accepted Answer

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

Question 4

Find the missing numerator and denominator.
-$$\frac { x ^ { 2 } - 16 } { x } \div \frac { ? } { ? } = \frac { ( x - 4 ) ( x + 2 ) } { x }$$

Accepted Answer

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

Question 5

Subtract.
-$$\frac { 2 x + 5 } { x ^ { 2 } + 5 x + 4 } - \frac { x + 1 } { x ^ { 2 } + 5 x + 4 }$$

Accepted Answer

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

Question 6

Subtract.
-$$\frac { 2 x } { x ^ { 2 } - 5 x + 6 } - \frac { 8 } { x ^ { 2 } - 6 x + 8 }$$

Accepted Answer

A)  $\frac { 2 x - 8 } { ( x - 2 ) ( x - 3 ) ( x - 4 ) }$ 
B)  $\frac { 2 } { ( x - 2 ) ( x - 3 ) }$ 
C)  $\frac { x - 6 } { ( x - 3 ) ( x - 4 ) }$ 
D)  $\frac { 2 ( x - 6 ) } { ( x - 3 ) ( x - 4 ) }$ 
A)  $\frac { 2 x - 8 } { ( x - 2 ) ( x - 3 ) ( x - 4 ) }$ 
B)  $\frac { 2 } { ( x - 2 ) ( x - 3 ) }$ 
C)  $\frac { x - 6 } { ( x - 3 ) ( x - 4 ) }$ 
D)  $\frac { 2 ( x - 6 ) } { ( x - 3 ) ( x - 4 ) }$

Question 7

For the given rational functions f(x) and g(x), f(x) +g(x).
-$$f ( x ) = \frac { x ^ { 2 } - 7 x } { x ^ { 2 } + 6 x + 9 } , g ( x ) = \frac { 6 x - 12 } { x ^ { 2 } + 6 x + 9 }$$

Accepted Answer

A)  $\frac { ( x - 4 ) ( x - 3 ) } { ( x + 3 ) ^ { 2 } }$ 
B)  $\frac { x - 4 } { x + 3 }$ 
C)  $\frac { x + 4 } { x + 3 }$ 
D)  $\frac { 1 } { x + 3 }$ 
A)  $\frac { ( x - 4 ) ( x - 3 ) } { ( x + 3 ) ^ { 2 } }$ 
B)  $\frac { x - 4 } { x + 3 }$ 
C)  $\frac { x + 4 } { x + 3 }$ 
D)  $\frac { 1 } { x + 3 }$

Question 8

For the given rational functions f(x) and g(x), f(x) -g(x).
-$$f ( x ) = \frac { 3 x ^ { 2 } + 12 } { x ^ { 2 } + 3 x - 4 } , g ( x ) = \frac { 13 x } { x ^ { 2 } + 3 x - 4 }$$

Accepted Answer

A)  $\frac { ( x + 3 ) ( 3 x + 4 ) } { ( x + 4 ) ( x - 1 ) }$ 
B)  $\frac { ( x - 3 ) ( 3 x + 4 ) } { ( x + 4 ) ( x - 1 ) }$ 
C)  $\frac { ( x - 3 ) ( 3 x - 4 ) } { ( x + 4 ) ( x - 1 ) }$ 
D)  $\frac { 3 x - 4 } { x - 1 }$ 
A)  $\frac { ( x + 3 ) ( 3 x + 4 ) } { ( x + 4 ) ( x - 1 ) }$ 
B)  $\frac { ( x - 3 ) ( 3 x + 4 ) } { ( x + 4 ) ( x - 1 ) }$ 
C)  $\frac { ( x - 3 ) ( 3 x - 4 ) } { ( x + 4 ) ( x - 1 ) }$ 
D)  $\frac { 3 x - 4 } { x - 1 }$

Question 9

Solve.
-The sum of a number and 5 times its reciprocal is 6. Find the number.

Accepted Answer

A)  5 
B)  1 or 5 
C)  6 
D)  1 
A)  5 
B)  1 or 5 
C)  6 
D)  1

Question 10

Subtract.
-$$\frac { 9 x + 6 } { x ^ { 2 } - 4 } - \frac { 5 x + 14 } { x ^ { 2 } - 4 }$$

Accepted Answer

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

Question 11

Evaluate the rational expression for the given value of the variable
-$\frac { 3 x + 3 } { 2 x ^ { 2 } - 6 x - 2 }$ for $x = - 4$

Accepted Answer

A)  $\frac { 5 } { 18 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $- \frac { 5 } { 18 }$ 
D)  $- \frac { 9 } { 10 }$ 
A)  $\frac { 5 } { 18 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $- \frac { 5 } { 18 }$ 
D)  $- \frac { 9 } { 10 }$

Question 12

Subtract.
-$$\frac { 4 x - 7 } { x ^ { 2 } + 7 x + 12 } - \frac { x - 3 } { x ^ { 2 } - 16 }$$

Accepted Answer

A)  $\frac { 5 x ^ { 2 } - 23 x + 19 } { ( x + 4 ) ( x - 4 ) ( x + 3 ) }$ 
B)  $\frac { 3 x ^ { 2 } - 23 x + 37 } { ( x + 4 ) ( x - 4 ) ( x + 3 }$ 
C)  $\frac { 5 x - 10 } { ( x + 4 ) ( x + 3 ) }$ 
D)  $\frac { 3 x - 4 } { ( x + 4 ) ( x - 4 ) }$ 
A)  $\frac { 5 x ^ { 2 } - 23 x + 19 } { ( x + 4 ) ( x - 4 ) ( x + 3 ) }$ 
B)  $\frac { 3 x ^ { 2 } - 23 x + 37 } { ( x + 4 ) ( x - 4 ) ( x + 3 }$ 
C)  $\frac { 5 x - 10 } { ( x + 4 ) ( x + 3 ) }$ 
D)  $\frac { 3 x - 4 } { ( x + 4 ) ( x - 4 ) }$

Question 13

Find all values of the variable for which the rational expression is undefined.
-$\frac { 7 } { x - 7 }$

Accepted Answer

A)  7 
B)  None 
C)  0 
D)  $- 7$ 
A)  7 
B)  None 
C)  0 
D)  $- 7$

Question 14

For the given functions f(x) and g(x), find f(x) ÷ g(x).
-$$f ( x ) = ( x - 6 ) , g ( x ) = \frac { 2 x ^ { 2 } - 6 x - 36 } { x ^ { 2 } - 9 x + 18 }$$

Accepted Answer

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

Question 15

Solve the problem.
-An experienced accountant can prepare a tax return in 17 hours. A novice accountant can do the job in 23 hours. How long will it take them to do the job working together?

Accepted Answer

A)  $65 \frac { 1 } { 6 }$ hours 
B)  $\frac { 1 } { 391 }$ hours 
C)  $\frac { 1 } { 40 }$ hours 
D)  $9 \frac { 31 } { 40 }$ hours 
A)  $65 \frac { 1 } { 6 }$ hours 
B)  $\frac { 1 } { 391 }$ hours 
C)  $\frac { 1 } { 40 }$ hours 
D)  $9 \frac { 31 } { 40 }$ hours

Question 16

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

Accepted Answer

A)  0 
B)  Undefined 
C)  $\frac { 2 } { 3 }$ 
D)  $- \frac { 2 } { 3 }$ 
A)  0 
B)  Undefined 
C)  $\frac { 2 } { 3 }$ 
D)  $- \frac { 2 } { 3 }$

Question 17

Solve the problem.
-Frank can type a report in 4 hours. James takes 7 hours to type it. How long will it take the two of them typing together?

Accepted Answer

A)  $\frac { 1 } { 11 }$ hours 
B)  $2 \frac { 6 } { 11 }$ hours 
C)  $\frac { 1 } { 28 }$ hours 
D)  $9 \frac { 1 } { 3 }$ hours 
A)  $\frac { 1 } { 11 }$ hours 
B)  $2 \frac { 6 } { 11 }$ hours 
C)  $\frac { 1 } { 28 }$ hours 
D)  $9 \frac { 1 } { 3 }$ hours

Question 18

Subtract.
-$$\frac { 3 x + 17 } { x - 3 } - \frac { 2 x + 5 } { x - 3 }$$

Accepted Answer

A)  $\frac { x + 22 } { x - 3 }$ 
B)  $\frac { x + 12 } { x - 3 }$ 
C)  $\frac { 2 x + 12 } { x - 3 }$ 
D)  $\frac { x + 22 } { 2 ( x - 3 ) }$ 
A)  $\frac { x + 22 } { x - 3 }$ 
B)  $\frac { x + 12 } { x - 3 }$ 
C)  $\frac { 2 x + 12 } { x - 3 }$ 
D)  $\frac { x + 22 } { 2 ( x - 3 ) }$

Question 19

Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { x ^ { 2 } - 7 x - 18 } { x ^ { 2 } - 3 x - 54 }$$

Accepted Answer

A)  $\frac { - 7 x - 18 } { - 3 x - 54 }$ 
B)  $- \frac { x ^ { 2 } - 7 x - 18 } { x ^ { 2 } - 3 x - 54 }$ 
C)  $\frac { - 7 x - 1 } { - 3 x - 3 }$ 
D)  $\frac { x + 2 } { x + 6 }$ 
A)  $\frac { - 7 x - 18 } { - 3 x - 54 }$ 
B)  $- \frac { x ^ { 2 } - 7 x - 18 } { x ^ { 2 } - 3 x - 54 }$ 
C)  $\frac { - 7 x - 1 } { - 3 x - 3 }$ 
D)  $\frac { x + 2 } { x + 6 }$

Question 20

Add.
-$\frac { 2 x + 8 } { x } + \frac { 6 x - 9 } { 7 x }$

Accepted Answer

A)  $\frac { 8 x + 47 } { 7 x }$ 
B)  $\frac { 20 x - 65 } { 7 x }$ 
C)  $\frac { 20 x + 47 } { 7 x }$ 
D)  $\frac { 20 x + 47 } { 7 x ^ { 2 } }$ 
A)  $\frac { 8 x + 47 } { 7 x }$ 
B)  $\frac { 20 x - 65 } { 7 x }$ 
C)  $\frac { 20 x + 47 } { 7 x }$ 
D)  $\frac { 20 x + 47 } { 7 x ^ { 2 } }$

Evaluate the rational expression for the given value of the variable - $\frac { x ^ { 2 } - 4 x } { x - 3 }$ for $x = 8$

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

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = \frac { 6 } { ( x - 6 ) } , g ( x ) = \frac { x ^ { 2 } - 3 x - 18 } { ( x + 3 ) ^ { 2 } }$

Find the missing numerator and denominator. - $\frac { x ^ { 2 } - 16 } { x } \div \frac { ? } { ? } = \frac { ( x - 4 ) ( x + 2 ) } { x }$

Subtract. - $\frac { 2 x + 5 } { x ^ { 2 } + 5 x + 4 } - \frac { x + 1 } { x ^ { 2 } + 5 x + 4 }$

Subtract. - $\frac { 2 x } { x ^ { 2 } - 5 x + 6 } - \frac { 8 } { x ^ { 2 } - 6 x + 8 }$

For the given rational functions f(x) and g(x), f(x) +g(x). - $f ( x ) = \frac { x ^ { 2 } - 7 x } { x ^ { 2 } + 6 x + 9 } , g ( x ) = \frac { 6 x - 12 } { x ^ { 2 } + 6 x + 9 }$

For the given rational functions f(x) and g(x), f(x) -g(x). - $f ( x ) = \frac { 3 x ^ { 2 } + 12 } { x ^ { 2 } + 3 x - 4 } , g ( x ) = \frac { 13 x } { x ^ { 2 } + 3 x - 4 }$

Solve. -The sum of a number and 5 times its reciprocal is 6. Find the number.

Subtract. - $\frac { 9 x + 6 } { x ^ { 2 } - 4 } - \frac { 5 x + 14 } { x ^ { 2 } - 4 }$

Evaluate the rational expression for the given value of the variable - $\frac { 3 x + 3 } { 2 x ^ { 2 } - 6 x - 2 }$ for $x = - 4$

Subtract. - $\frac { 4 x - 7 } { x ^ { 2 } + 7 x + 12 } - \frac { x - 3 } { x ^ { 2 } - 16 }$

Find all values of the variable for which the rational expression is undefined. - $\frac { 7 } { x - 7 }$

For the given functions f(x) and g(x), find f(x) ÷ g(x). - $f ( x ) = ( x - 6 ) , g ( x ) = \frac { 2 x ^ { 2 } - 6 x - 36 } { x ^ { 2 } - 9 x + 18 }$

Solve the problem. -An experienced accountant can prepare a tax return in 17 hours. A novice accountant can do the job in 23 hours. How long will it take them to do the job working together?

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

Solve the problem. -Frank can type a report in 4 hours. James takes 7 hours to type it. How long will it take the two of them typing together?

Subtract. - $\frac { 3 x + 17 } { x - 3 } - \frac { 2 x + 5 } { x - 3 }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { x ^ { 2 } - 7 x - 18 } { x ^ { 2 } - 3 x - 54 }$

Add. - $\frac { 2 x + 8 } { x } + \frac { 6 x - 9 } { 7 x }$

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

Evaluate the rational expression for the given value of the variable - x2−4xx−3\frac { x ^ { 2 } - 4 x } { x - 3 }x−3x2−4x​ for x=8x = 8x=8

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

For the given functions f(x) and g(x), find f(x) ∙ g(x). - f(x)=6(x−6),g(x)=x2−3x−18(x+3)2f ( x ) = \frac { 6 } { ( x - 6 ) } , g ( x ) = \frac { x ^ { 2 } - 3 x - 18 } { ( x + 3 ) ^ { 2 } }f(x)=(x−6)6​,g(x)=(x+3)2x2−3x−18​

Find the missing numerator and denominator. - x2−16x÷??=(x−4)(x+2)x\frac { x ^ { 2 } - 16 } { x } \div \frac { ? } { ? } = \frac { ( x - 4 ) ( x + 2 ) } { x }xx2−16​÷??​=x(x−4)(x+2)​

Subtract. - 2x+5x2+5x+4−x+1x2+5x+4\frac { 2 x + 5 } { x ^ { 2 } + 5 x + 4 } - \frac { x + 1 } { x ^ { 2 } + 5 x + 4 }x2+5x+42x+5​−x2+5x+4x+1​

Subtract. - 2xx2−5x+6−8x2−6x+8\frac { 2 x } { x ^ { 2 } - 5 x + 6 } - \frac { 8 } { x ^ { 2 } - 6 x + 8 }x2−5x+62x​−x2−6x+88​

For the given rational functions f(x) and g(x), f(x) +g(x). - f(x)=x2−7xx2+6x+9,g(x)=6x−12x2+6x+9f ( x ) = \frac { x ^ { 2 } - 7 x } { x ^ { 2 } + 6 x + 9 } , g ( x ) = \frac { 6 x - 12 } { x ^ { 2 } + 6 x + 9 }f(x)=x2+6x+9x2−7x​,g(x)=x2+6x+96x−12​

For the given rational functions f(x) and g(x), f(x) -g(x). - f(x)=3x2+12x2+3x−4,g(x)=13xx2+3x−4f ( x ) = \frac { 3 x ^ { 2 } + 12 } { x ^ { 2 } + 3 x - 4 } , g ( x ) = \frac { 13 x } { x ^ { 2 } + 3 x - 4 }f(x)=x2+3x−43x2+12​,g(x)=x2+3x−413x​