Question 1

Add. Simplify, if possible.
-$$\frac { m ^ { 2 } - 9 m } { m - 3 } + \frac { 18 } { m - 3 }$$

Accepted Answer

A)  $m - 3$ 
B)  $\frac { m ^ { 2 } - 9 m + 18 } { m - 3 }$ 
C)  $m + 6$ 
D)  $m - 6$ 
A)  $m - 3$ 
B)  $\frac { m ^ { 2 } - 9 m + 18 } { m - 3 }$ 
C)  $m + 6$ 
D)  $m - 6$

Question 2

Find the LCM.
-$15 x y , 9 x ^ { 2 }$

Accepted Answer

A)  $45 x ^ { 2 } y$ 
B)  $45 \mathrm { xy } ^ { 3 }$ 
C)  $45 \mathrm { xy } ^ { 2 }$ 
D)  $45 \mathrm { x } ^ { 3 } \mathrm { y }$ 
A)  $45 x ^ { 2 } y$ 
B)  $45 \mathrm { xy } ^ { 3 }$ 
C)  $45 \mathrm { xy } ^ { 2 }$ 
D)  $45 \mathrm { x } ^ { 3 } \mathrm { y }$

Question 3

Simplify.
-$\frac { 2 m ^ { 2 } + 2 m } { 6 m ^ { 2 } + 8 m }$

Accepted Answer

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

Question 4

Find the LCM.
-$t , t - 7$

Accepted Answer

A)  $t ( t - 7 )$ 
B)  $t$ 
C)  6 
D)  $t - 7$ 
A)  $t ( t - 7 )$ 
B)  $t$ 
C)  6 
D)  $t - 7$

Question 5

Add, first finding the LCD. Simplify, if possible.
-$$\frac { 7 } { 12 } + \frac { 1 } { 54 }$$

Accepted Answer

A)  $\frac { 65 } { 108 }$ 
B)  $\frac { 4 } { 33 }$ 
C)  $\frac { 65 } { 11 }$ 
D)  $\frac { 1 } { 81 }$ 
A)  $\frac { 65 } { 108 }$ 
B)  $\frac { 4 } { 33 }$ 
C)  $\frac { 65 } { 11 }$ 
D)  $\frac { 1 } { 81 }$

Question 6

Multiply and, if possible, simplify.
-$$\frac { k ^ { 2 } + 7 k + 12 } { k ^ { 2 } + 10 k + 24 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 3 k - 18 }$$

Accepted Answer

A)  $\frac { k ^ { 2 } + 6 k } { k - 6 }$ 
B)  $\frac { k } { k - 6 }$ 
C)  $\frac { 1 } { k - 6 }$ 
D)  $\frac { k } { k ^ { 2 } + 10 k + 24 }$ 
A)  $\frac { k ^ { 2 } + 6 k } { k - 6 }$ 
B)  $\frac { k } { k - 6 }$ 
C)  $\frac { 1 } { k - 6 }$ 
D)  $\frac { k } { k ^ { 2 } + 10 k + 24 }$

Question 7

Add. Simplify, if possible.
-$$\frac { 3 } { r } + \frac { 8 } { r - 7 }$$

Accepted Answer

A)  $\frac { 11 r - 21 } { r ( 7 - r ) }$ 
B)  $\frac { 21 r - 11 } { r ( 7 - r ) }$ 
C)  $\frac { 11 r - 21 } { r ( r - 7 ) }$ 
D)  $\frac { 21 r - 11 } { r ( r - 7 ) }$ 
A)  $\frac { 11 r - 21 } { r ( 7 - r ) }$ 
B)  $\frac { 21 r - 11 } { r ( 7 - r ) }$ 
C)  $\frac { 11 r - 21 } { r ( r - 7 ) }$ 
D)  $\frac { 21 r - 11 } { r ( r - 7 ) }$

Question 8

Find the LCM.
-$m ^ { 2 } - 3 m , m ^ { 2 } - 7 m + 12$

Accepted Answer

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

Question 9

Add. Simplify, if possible.
-$\frac { 9 } { 9 x ^ { 2 } } + \frac { 3 } { 9 x ^ { 2 } }$

Accepted Answer

A)  4 
B)  $\frac { 3 } { 4 x ^ { 2 } }$ 
C)  $\frac { 4 } { 3 x ^ { 2 } }$ 
D)  $\frac { 4 } { 3 x ^ { 4 } }$ 
A)  4 
B)  $\frac { 3 } { 4 x ^ { 2 } }$ 
C)  $\frac { 4 } { 3 x ^ { 2 } }$ 
D)  $\frac { 4 } { 3 x ^ { 4 } }$

Question 10

Simplify.
-$$\frac { x - 4 + \frac { 4 } { x } } { x - 7 + \frac { 10 } { x } }$$

Accepted Answer

A)  $\frac { x - 2 } { x - 5 }$ 
B)  $\frac { ( x - 2 ) ^ { 2 } } { x - 5 }$ 
C)  $\frac { x - 2 } { x ^ { 2 } - 5 x }$ 
D)  $\frac { x ^ { 2 } - 4 x + 4 } { x ^ { 2 } - 7 x + 10 }$ 
A)  $\frac { x - 2 } { x - 5 }$ 
B)  $\frac { ( x - 2 ) ^ { 2 } } { x - 5 }$ 
C)  $\frac { x - 2 } { x ^ { 2 } - 5 x }$ 
D)  $\frac { x ^ { 2 } - 4 x + 4 } { x ^ { 2 } - 7 x + 10 }$

Question 11

Find the LCM.
-$50 x ^ { 5 } y , 60 x ^ { 4 } y ^ { 3 } , 30 x ^ { 2 } y ^ { 4 }$

Accepted Answer

A)  $300 x ^ { 5 } y ^ { 4 }$ 
B)  $60 x ^ { 5 } y$ 
C)  $150 \mathrm { x } ^ { 20 } \mathrm { y } ^ { 12 }$ 
D)  $100 x ^ { 5 } y ^ { 4 }$ 
A)  $300 x ^ { 5 } y ^ { 4 }$ 
B)  $60 x ^ { 5 } y$ 
C)  $150 \mathrm { x } ^ { 20 } \mathrm { y } ^ { 12 }$ 
D)  $100 x ^ { 5 } y ^ { 4 }$

Question 12

Multiply and, if possible, simplify.
-$\frac { 2 z ^ { 3 } } { 4 } \cdot \frac { 8 } { z ^ { 2 } }$

Accepted Answer

A)  $\frac { 4 } { \mathrm { z } }$ 
B)  $4 \mathrm { z }$ 
C)  $\frac { z } { 4 }$ 
D)  $\frac { 4 z ^ { 2 } } { z ^ { 3 } }$ 
A)  $\frac { 4 } { \mathrm { z } }$ 
B)  $4 \mathrm { z }$ 
C)  $\frac { z } { 4 }$ 
D)  $\frac { 4 z ^ { 2 } } { z ^ { 3 } }$

Question 13

Find the LCM.
-$$\mathrm { n } , 9 + \mathrm { n } , 9 - \mathrm { n }$$

Accepted Answer

A)  $81 \mathrm { n } ^ { 2 }$ 
B)  $n ^ { 2 } + 81$ 
C)  $n + 9$ 
D)  $n ( 9 + n ) ( 9 - n )$ 
A)  $81 \mathrm { n } ^ { 2 }$ 
B)  $n ^ { 2 } + 81$ 
C)  $n + 9$ 
D)  $n ( 9 + n ) ( 9 - n )$

Question 14

Subtract. Simplify, if possible.
-$$\frac { 7 x } { x ^ { 2 } - 9 } - \frac { x } { x - 3 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 9 }$ 
B)  $\frac { - x ^ { 2 } + 10 x } { x ^ { 2 } - 9 }$ 
C)  $\frac { x ^ { 2 } + 10 x } { x ^ { 2 } - 9 }$ 
D)  $\frac { - x ^ { 2 } + 4 x } { x ^ { 2 } - 9 }$ 
A)  $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 9 }$ 
B)  $\frac { - x ^ { 2 } + 10 x } { x ^ { 2 } - 9 }$ 
C)  $\frac { x ^ { 2 } + 10 x } { x ^ { 2 } - 9 }$ 
D)  $\frac { - x ^ { 2 } + 4 x } { x ^ { 2 } - 9 }$

Question 15

Find the LCM.
-54,12

Accepted Answer

A)  54 
B)  18 
C)  36 
D)  108 
A)  54 
B)  18 
C)  36 
D)  108

Question 16

Add. Simplify, if possible.
-$$\frac { 7 } { r } + \frac { 9 } { r - 5 }$$

Accepted Answer

A)  $\frac { 16 r - 35 } { r ( r - 5 ) }$ 
B)  $\frac { 16 r - 35 } { r ( 5 - r ) }$ 
C)  $\frac { 35 r - 16 } { r ( r - 5 ) }$ 
D)  $\frac { 35 r - 16 } { r ( 5 - r ) }$ 
A)  $\frac { 16 r - 35 } { r ( r - 5 ) }$ 
B)  $\frac { 16 r - 35 } { r ( 5 - r ) }$ 
C)  $\frac { 35 r - 16 } { r ( r - 5 ) }$ 
D)  $\frac { 35 r - 16 } { r ( 5 - r ) }$

Question 17

Find all numbers for which the rational expression is not defined.
-$$\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 2 x - 24 }$$

Accepted Answer

A)  $x = - 4$ and $x = 6$ 
B)  $x = 4$ and $x = - 4$ 
C)  $x = 4$ and $x = - 6$ 
D)  $x = 0$ 
A)  $x = - 4$ and $x = 6$ 
B)  $x = 4$ and $x = - 4$ 
C)  $x = 4$ and $x = - 6$ 
D)  $x = 0$

Question 18

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

Accepted Answer

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

Question 19

Simplify.
-$$\frac { \frac { 1 } { x ^ { 2 } } - \frac { 4 } { y ^ { 2 } } } { 9 y - 18 x }$$

Accepted Answer

A)  $\frac { x + 2 y } { 9 x ^ { 2 } y }$ 
B)  $\frac { y ^ { 2 } + 2 x } { 9 x ^ { 2 } }$ 
C)  $9 x - 18 y ^ { 2 }$ 
D)  $\frac { y + 2 x } { 9 x ^ { 2 } y ^ { 2 } }$ 
A)  $\frac { x + 2 y } { 9 x ^ { 2 } y }$ 
B)  $\frac { y ^ { 2 } + 2 x } { 9 x ^ { 2 } }$ 
C)  $9 x - 18 y ^ { 2 }$ 
D)  $\frac { y + 2 x } { 9 x ^ { 2 } y ^ { 2 } }$

Question 20

Add. Simplify, if possible.
-$$\frac { 4 } { 8 } + \frac { 6 } { 8 }$$

Accepted Answer

A)  5 
B)  $\frac { 5 } { 2 }$ 
C)  $\frac { 4 } { 5 }$ 
D)  $\frac { 5 } { 4 }$ 
A)  5 
B)  $\frac { 5 } { 2 }$ 
C)  $\frac { 4 } { 5 }$ 
D)  $\frac { 5 } { 4 }$

Add. Simplify, if possible. - $\frac { m ^ { 2 } - 9 m } { m - 3 } + \frac { 18 } { m - 3 }$

Find the LCM. - $15 x y , 9 x ^ { 2 }$

Simplify. - $\frac { 2 m ^ { 2 } + 2 m } { 6 m ^ { 2 } + 8 m }$

Find the LCM. - $t , t - 7$

Add, first finding the LCD. Simplify, if possible. - $\frac { 7 } { 12 } + \frac { 1 } { 54 }$

Multiply and, if possible, simplify. - $\frac { k ^ { 2 } + 7 k + 12 } { k ^ { 2 } + 10 k + 24 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 3 k - 18 }$

Add. Simplify, if possible. - $\frac { 3 } { r } + \frac { 8 } { r - 7 }$

Find the LCM. - $m ^ { 2 } - 3 m , m ^ { 2 } - 7 m + 12$

Add. Simplify, if possible. - $\frac { 9 } { 9 x ^ { 2 } } + \frac { 3 } { 9 x ^ { 2 } }$

Simplify. - $\frac { x - 4 + \frac { 4 } { x } } { x - 7 + \frac { 10 } { x } }$

Find the LCM. - $50 x ^ { 5 } y , 60 x ^ { 4 } y ^ { 3 } , 30 x ^ { 2 } y ^ { 4 }$

Multiply and, if possible, simplify. - $\frac { 2 z ^ { 3 } } { 4 } \cdot \frac { 8 } { z ^ { 2 } }$

Find the LCM. - $\mathrm { n } , 9 + \mathrm { n } , 9 - \mathrm { n }$

Subtract. Simplify, if possible. - $\frac { 7 x } { x ^ { 2 } - 9 } - \frac { x } { x - 3 }$

Find the LCM. -54,12

Add. Simplify, if possible. - $\frac { 7 } { r } + \frac { 9 } { r - 5 }$

Find all numbers for which the rational expression is not defined. - $\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 2 x - 24 }$

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

Simplify. - $\frac { \frac { 1 } { x ^ { 2 } } - \frac { 4 } { y ^ { 2 } } } { 9 y - 18 x }$

Add. Simplify, if possible. - $\frac { 4 } { 8 } + \frac { 6 } { 8 }$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 6: Rational Expressions and Equations

Add. Simplify, if possible. - m2−9mm−3+18m−3\frac { m ^ { 2 } - 9 m } { m - 3 } + \frac { 18 } { m - 3 }m−3m2−9m​+m−318​

Find the LCM. - 15xy,9x215 x y , 9 x ^ { 2 }15xy,9x2

Simplify. - 2m2+2m6m2+8m\frac { 2 m ^ { 2 } + 2 m } { 6 m ^ { 2 } + 8 m }6m2+8m2m2+2m​

Find the LCM. - t,t−7t , t - 7t,t−7

Add, first finding the LCD. Simplify, if possible. - 712+154\frac { 7 } { 12 } + \frac { 1 } { 54 }127​+541​

Multiply and, if possible, simplify. - k2+7k+12k2+10k+24⋅k2+6kk2−3k−18\frac { k ^ { 2 } + 7 k + 12 } { k ^ { 2 } + 10 k + 24 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 3 k - 18 }k2+10k+24k2+7k+12​⋅k2−3k−18k2+6k​

Add. Simplify, if possible. - 3r+8r−7\frac { 3 } { r } + \frac { 8 } { r - 7 }r3​+r−78​

Find the LCM. - m2−3m,m2−7m+12m ^ { 2 } - 3 m , m ^ { 2 } - 7 m + 12m2−3m,m2−7m+12

Add. Simplify, if possible. - 99x2+39x2\frac { 9 } { 9 x ^ { 2 } } + \frac { 3 } { 9 x ^ { 2 } }9x29​+9x23​

Simplify. - x−4+4xx−7+10x\frac { x - 4 + \frac { 4 } { x } } { x - 7 + \frac { 10 } { x } }x−7+x10​x−4+x4​​

Find the LCM. - 50x5y,60x4y3,30x2y450 x ^ { 5 } y , 60 x ^ { 4 } y ^ { 3 } , 30 x ^ { 2 } y ^ { 4 }50x5y,60x4y3,30x2y4

Multiply and, if possible, simplify. - 2z34⋅8z2\frac { 2 z ^ { 3 } } { 4 } \cdot \frac { 8 } { z ^ { 2 } }42z3​⋅z28​

Find the LCM. - n,9+n,9−n\mathrm { n } , 9 + \mathrm { n } , 9 - \mathrm { n }n,9+n,9−n

Subtract. Simplify, if possible. - 7xx2−9−xx−3\frac { 7 x } { x ^ { 2 } - 9 } - \frac { x } { x - 3 }x2−97x​−x−3x​