Question 1

Add or subtract.
-$$\frac { x ^ { 2 } - 2 x } { x - 8 } + \frac { 4 x + 16 } { 8 - x }$$

Accepted Answer

A)  $x - 2$ 
B)  $x + 2$ 
C)  $- \frac { x ^ { 2 } + 2 x + 16 } { x - 8 }$ 
D)  $\frac { x ^ { 2 } + 2 x + 16 } { x - 8 }$ 
A)  $x - 2$ 
B)  $x + 2$ 
C)  $- \frac { x ^ { 2 } + 2 x + 16 } { x - 8 }$ 
D)  $\frac { x ^ { 2 } + 2 x + 16 } { x - 8 }$

Question 2

Add.
-$$\frac { 12 } { x } + \frac { 7 } { 6 x }$$

Accepted Answer

A)  $\frac { 79 x } { 6 }$ 
B)  $\frac { 19 } { x ^ { 2 } }$ 
C)  $\frac { 79 } { 6 x }$ 
D)  $- \frac { 79 } { x }$ 
A)  $\frac { 79 x } { 6 }$ 
B)  $\frac { 19 } { x ^ { 2 } }$ 
C)  $\frac { 79 } { 6 x }$ 
D)  $- \frac { 79 } { x }$

Question 3

Solve.
-If y varies inversely as the square of x. If y = 2 when x = 8 $\text { find } y \text { when }$

Accepted Answer

A)  4 
B)  8 
C)  32 
D)  16 
A)  4 
B)  8 
C)  32 
D)  16

Question 4

Subtract.
-$$\frac { 3 x } { 4 x - 3 } - \frac { 3 } { 4 x - 3 }$$

Accepted Answer

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

Question 5

Find all values of the variable for which the rational expression is undefined.
-$\frac { x - 9 } { 7 - x }$

Accepted Answer

A)  7 
B)  None 
C)  7,9 
D)  $- 7$ 
A)  7 
B)  None 
C)  7,9 
D)  $- 7$

Question 6

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

Accepted Answer

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

Question 7

Add.
-$$\frac { 3 } { 14 x } + \frac { 9 } { 10 x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 12 } { 140 x ^ { 2 } }$ 
B)  $\frac { 15 x + 63 } { 70 x ^ { 2 } }$ 
C)  $\frac { 12 } { 14 x + 10 x ^ { 2 } }$ 
D)  $\frac { 108 } { 70 x ^ { 2 } }$ 
A)  $\frac { 12 } { 140 x ^ { 2 } }$ 
B)  $\frac { 15 x + 63 } { 70 x ^ { 2 } }$ 
C)  $\frac { 12 } { 14 x + 10 x ^ { 2 } }$ 
D)  $\frac { 108 } { 70 x ^ { 2 } }$

Question 8

Simplify the complex fraction.
-$$\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$$

Accepted Answer

A)  $\frac { x } { 16 }$ 
B)  1 
C)  16 
D)  $\frac { 16 } { x }$ 
A)  $\frac { x } { 16 }$ 
B)  1 
C)  16 
D)  $\frac { 16 } { x }$

Question 9

Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { 7 x - 14 } { 4 - x ^ { 2 } } \cdot \frac { 6 x ^ { 2 } + 7 x + 1 } { 42 x + 7 }$$

Accepted Answer

A)  $\frac { x + 1 } { 2 - x }$ 
B)  $- \frac { 7 ( x + 1 ) } { x + 2 }$ 
C)  $\frac { x + 1 } { x + 2 }$ 
D)  $- \frac { x + 1 } { x + 2 }$ 
A)  $\frac { x + 1 } { 2 - x }$ 
B)  $- \frac { 7 ( x + 1 ) } { x + 2 }$ 
C)  $\frac { x + 1 } { x + 2 }$ 
D)  $- \frac { x + 1 } { x + 2 }$

Question 10

For the given functions f(x) and g(x), find f(x) ÷ g(x).
-$$f ( x ) = \frac { x ^ { 2 } + 9 x + 20 } { x ^ { 2 } + 10 x + 24 } , g ( x ) = \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 4 x - 12 }$$

Accepted Answer

A)  $x - 2$ 
B)  $\frac { x } { x ^ { 2 } + 10 x + 24 }$ 
C)  $\frac { x - 2 } { x }$ 
D)  $\frac { x - 2 } { x ^ { 2 } + 6 x }$ 
A)  $x - 2$ 
B)  $\frac { x } { x ^ { 2 } + 10 x + 24 }$ 
C)  $\frac { x - 2 } { x }$ 
D)  $\frac { x - 2 } { x ^ { 2 } + 6 x }$

Question 11

Find all values of the variable for which the rational expression is undefined.
-$\frac { 2 } { x + 8 }$

Accepted Answer

A)  $- 8$ 
B)  8 
C)  None 
D)  0 
A)  $- 8$ 
B)  8 
C)  None 
D)  0

Question 12

Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { ( x + 2 ) ( x - 3 ) } { ( x - 3 ) ( x + 9 ) }$$

Accepted Answer

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

Question 13

Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { x ^ { 2 } + 5 x + 4 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 4 x - 5 }$$

Accepted Answer

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

Question 14

Find all values of the variable for which the rational expression is undefined.
-$\frac { 19 } { x - 9 }$

Accepted Answer

A)  19 
B)  $- 9$ 
C)  9 
D)  0 
A)  19 
B)  $- 9$ 
C)  9 
D)  0

Question 15

Simplify the complex fraction.
-$$\frac { 1 + \frac { 3 } { 5 } } { 1 + \frac { 1 } { 10 } }$$

Accepted Answer

A)  $\frac { 8 } { 11 }$ 
B)  $\frac { 16 } { 3 }$ 
C)  $\frac { 16 } { 11 }$ 
D)  $\frac { 4 } { 3 }$ 
A)  $\frac { 8 } { 11 }$ 
B)  $\frac { 16 } { 3 }$ 
C)  $\frac { 16 } { 11 }$ 
D)  $\frac { 4 } { 3 }$

Question 16

For the given rational functions f(x) and g(x), f(x) +g(x).
-$$f ( x ) = \frac { 7 x + 4 } { 7 x + 9 } , g ( x ) = \frac { 7 x + 14 } { 7 x + 9 }$$

Accepted Answer

A)  $\frac { 8 x + 10 } { 7 x + 9 }$ 
B)  $\frac { 2 } { 7 x + 9 }$ 
C)  2 
D)  1 
A)  $\frac { 8 x + 10 } { 7 x + 9 }$ 
B)  $\frac { 2 } { 7 x + 9 }$ 
C)  2 
D)  1

Question 17

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

Accepted Answer

A)  $\frac { x + 6 } { 2 \left( x ^ { 2 } + 7 x + 6 \right) }$ 
B)  $\frac { 1 } { x - 1 }$ 
C)  $\frac { x + 6 } { x ^ { 2 } + 7 x + 6 }$ 
D)  $\frac { 1 } { x + 1 }$ 
A)  $\frac { x + 6 } { 2 \left( x ^ { 2 } + 7 x + 6 \right) }$ 
B)  $\frac { 1 } { x - 1 }$ 
C)  $\frac { x + 6 } { x ^ { 2 } + 7 x + 6 }$ 
D)  $\frac { 1 } { x + 1 }$

Question 18

Divide.
-$$\frac { x ^ { 2 } - 1 } { x } \div \frac { x - 1 } { x - 3 }$$

Accepted Answer

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

Question 19

Add or subtract.
-$$\frac { 56 } { 6 x - 48 } + \frac { 7 x } { 48 - 6 x }$$

Accepted Answer

A)  $- \frac { 7 } { 6 }$ 
B)  $- \frac { 7 ( x + 8 ) } { 6 ( x - 8 ) }$ 
C)  $\frac { 7 } { 6 }$ 
D)  $\frac { 7 ( x + 8 ) } { 6 ( x - 8 ) }$ 
A)  $- \frac { 7 } { 6 }$ 
B)  $- \frac { 7 ( x + 8 ) } { 6 ( x - 8 ) }$ 
C)  $\frac { 7 } { 6 }$ 
D)  $\frac { 7 ( x + 8 ) } { 6 ( x - 8 ) }$

Question 20

Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { 4 x ^ { 2 } - 64 } { 32 - 8 x }$$

Accepted Answer

A)  $- \frac { x + 4 } { 2 }$ 
B)  $- 2 ( x + 4 )$ 
C)  $\frac { x ^ { 2 } - 16 } { 4 - x }$ 
D)  $\frac { x + 4 } { 2 }$ 
A)  $- \frac { x + 4 } { 2 }$ 
B)  $- 2 ( x + 4 )$ 
C)  $\frac { x ^ { 2 } - 16 } { 4 - x }$ 
D)  $\frac { x + 4 } { 2 }$

Add or subtract. - $\frac { x ^ { 2 } - 2 x } { x - 8 } + \frac { 4 x + 16 } { 8 - x }$

Add. - $\frac { 12 } { x } + \frac { 7 } { 6 x }$

Solve. -If y varies inversely as the square of x. If y = 2 when x = 8 $\text { find } y \text { when }$

Subtract. - $\frac { 3 x } { 4 x - 3 } - \frac { 3 } { 4 x - 3 }$

Find all values of the variable for which the rational expression is undefined. - $\frac { x - 9 } { 7 - x }$

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

Add. - $\frac { 3 } { 14 x } + \frac { 9 } { 10 x ^ { 2 } }$

Simplify the complex fraction. - $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { 7 x - 14 } { 4 - x ^ { 2 } } \cdot \frac { 6 x ^ { 2 } + 7 x + 1 } { 42 x + 7 }$

For the given functions f(x) and g(x), find f(x) ÷ g(x). - $f ( x ) = \frac { x ^ { 2 } + 9 x + 20 } { x ^ { 2 } + 10 x + 24 } , g ( x ) = \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 4 x - 12 }$

Find all values of the variable for which the rational expression is undefined. - $\frac { 2 } { x + 8 }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { ( x + 2 ) ( x - 3 ) } { ( x - 3 ) ( x + 9 ) }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { x ^ { 2 } + 5 x + 4 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 4 x - 5 }$

Find all values of the variable for which the rational expression is undefined. - $\frac { 19 } { x - 9 }$

Simplify the complex fraction. - $\frac { 1 + \frac { 3 } { 5 } } { 1 + \frac { 1 } { 10 } }$

For the given rational functions f(x) and g(x), f(x) +g(x). - $f ( x ) = \frac { 7 x + 4 } { 7 x + 9 } , g ( x ) = \frac { 7 x + 14 } { 7 x + 9 }$

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

Divide. - $\frac { x ^ { 2 } - 1 } { x } \div \frac { x - 1 } { x - 3 }$

Add or subtract. - $\frac { 56 } { 6 x - 48 } + \frac { 7 x } { 48 - 6 x }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { 4 x ^ { 2 } - 64 } { 32 - 8 x }$

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

Add or subtract. - x2−2xx−8+4x+168−x\frac { x ^ { 2 } - 2 x } { x - 8 } + \frac { 4 x + 16 } { 8 - x }x−8x2−2x​+8−x4x+16​

Add. - 12x+76x\frac { 12 } { x } + \frac { 7 } { 6 x }x12​+6x7​

Solve. -If y varies inversely as the square of x. If y = 2 when x = 8 find y when \text { find } y \text { when } find y when

Subtract. - 3x4x−3−34x−3\frac { 3 x } { 4 x - 3 } - \frac { 3 } { 4 x - 3 }4x−33x​−4x−33​

Find all values of the variable for which the rational expression is undefined. - x−97−x\frac { x - 9 } { 7 - x }7−xx−9​

Simplify the rational expression. (Assume the denominator is nonzero.) - (x+2)(x−2)x+2\frac { ( x + 2 ) ( x - 2 ) } { x + 2 }x+2(x+2)(x−2)​

Add. - 314x+910x2\frac { 3 } { 14 x } + \frac { 9 } { 10 x ^ { 2 } }14x3​+10x29​

Simplify the complex fraction. - 4+2xx4+18\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }4x​+81​4+x2​​

Simplify the rational expression. (Assume the denominator is nonzero.) - 7x−144−x2⋅6x2+7x+142x+7\frac { 7 x - 14 } { 4 - x ^ { 2 } } \cdot \frac { 6 x ^ { 2 } + 7 x + 1 } { 42 x + 7 }4−x27x−14​⋅42x+76x2+7x+1​

For the given functions f(x) and g(x), find f(x) ÷ g(x). - f(x)=x2+9x+20x2+10x+24,g(x)=x2+5xx2+4x−12f ( x ) = \frac { x ^ { 2 } + 9 x + 20 } { x ^ { 2 } + 10 x + 24 } , g ( x ) = \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 4 x - 12 }f(x)=x2+10x+24x2+9x+20​,g(x)=x2+4x−12x2+5x​

Find all values of the variable for which the rational expression is undefined. - 2x+8\frac { 2 } { x + 8 }x+82​

Simplify the rational expression. (Assume the denominator is nonzero.) - (x+2)(x−3)(x−3)(x+9)\frac { ( x + 2 ) ( x - 3 ) } { ( x - 3 ) ( x + 9 ) }(x−3)(x+9)(x+2)(x−3)​

Simplify the rational expression. (Assume the denominator is nonzero.) - x2+5x+4x2+7x+12⋅x2−8x+15x2−4x−5\frac { x ^ { 2 } + 5 x + 4 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 4 x - 5 }x2+7x+12x2+5x+4​⋅x2−4x−5x2−8x+15​

Find all values of the variable for which the rational expression is undefined. - 19x−9\frac { 19 } { x - 9 }x−919​

Simplify the complex fraction. - 1+351+110\frac { 1 + \frac { 3 } { 5 } } { 1 + \frac { 1 } { 10 } }1+101​1+53​​

For the given rational functions f(x) and g(x), f(x) +g(x). - f(x)=7x+47x+9,g(x)=7x+147x+9f ( x ) = \frac { 7 x + 4 } { 7 x + 9 } , g ( x ) = \frac { 7 x + 14 } { 7 x + 9 }f(x)=7x+97x+4​,g(x)=7x+97x+14​

Add. - xx2+7x+6+6x2+7x+6\frac { x } { x ^ { 2 } + 7 x + 6 } + \frac { 6 } { x ^ { 2 } + 7 x + 6 }x2+7x+6x​+x2+7x+66​

Divide. - x2−1x÷x−1x−3\frac { x ^ { 2 } - 1 } { x } \div \frac { x - 1 } { x - 3 }xx2−1​÷x−3x−1​

Add or subtract. - 566x−48+7x48−6x\frac { 56 } { 6 x - 48 } + \frac { 7 x } { 48 - 6 x }6x−4856​+48−6x7x​

Simplify the rational expression. (Assume the denominator is nonzero.) - 4x2−6432−8x\frac { 4 x ^ { 2 } - 64 } { 32 - 8 x }32−8x4x2−64​