Question 1

Perform the indicated operation. Simplify, if possible.
-$$\frac { - 16 x } { 5 ( 4 x + 1 ) } + \frac { 1 } { 5 x ( 4 x + 1 ) } - \frac { 5 } { x }$$

Accepted Answer

A)  $\frac { - 16 x ^ { 2 } - 100 x - 24 } { 5 x }$ 
B)  $- \frac { 4 ( x + 6 ) } { 5 x }$ 
C)  $- \frac { 4 ( x + 6 ) } { 20 x ^ { 2 } + 5 x }$ 
D)  $\frac { - 16 x ^ { 2 } - 100 x - 24 } { 20 x ^ { 2 } + 5 x }$ 
A)  $\frac { - 16 x ^ { 2 } - 100 x - 24 } { 5 x }$ 
B)  $- \frac { 4 ( x + 6 ) } { 5 x }$ 
C)  $- \frac { 4 ( x + 6 ) } { 20 x ^ { 2 } + 5 x }$ 
D)  $\frac { - 16 x ^ { 2 } - 100 x - 24 } { 20 x ^ { 2 } + 5 x }$

Question 2

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

Accepted Answer

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

Question 3

Add. Simplify, if possible.
-$\frac { 2 } { 15 x } + \frac { 4 } { 21 x ^ { 2 } }$

Accepted Answer

A)  $\frac { 48 } { 105 x ^ { 2 } }$ 
B)  $\frac { 2 ( 7 x + 10 ) } { 105 x ^ { 2 } }$ 
C)  $\frac { 6 } { 15 x + 21 x ^ { 2 } }$ 
D)  $\frac { 6 } { 315 x ^ { 2 } }$ 
A)  $\frac { 48 } { 105 x ^ { 2 } }$ 
B)  $\frac { 2 ( 7 x + 10 ) } { 105 x ^ { 2 } }$ 
C)  $\frac { 6 } { 15 x + 21 x ^ { 2 } }$ 
D)  $\frac { 6 } { 315 x ^ { 2 } }$

Question 4

Find an equation of variation in which the following are true.
-$y$ varies directly as $x$ and inversely as $z$, and $y = 18$ when $x = 2$ and $z = 9$.

Accepted Answer

A)  $y = \frac { 81 x } { z }$ 
B)  $y = \frac { 85 x } { z }$ 
C)  $y = 84 x z$ 
D)  $y = \frac { 80 z } { x }$ 
A)  $y = \frac { 81 x } { z }$ 
B)  $y = \frac { 85 x } { z }$ 
C)  $y = 84 x z$ 
D)  $y = \frac { 80 z } { x }$

Question 5

Solve the equation.
-$$\frac { x - 2 } { x + 4 } = \frac { 1 } { 5 }$$

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  $- \frac { 3 } { 2 }$ 
C)  $\frac { 7 } { 3 }$ 
D)  $\frac { 7 } { 2 }$ 
A)  $\frac { 3 } { 2 }$ 
B)  $- \frac { 3 } { 2 }$ 
C)  $\frac { 7 } { 3 }$ 
D)  $\frac { 7 } { 2 }$

Question 6

Find an equation of variation in which the following are true.
-$y$ varies directly as the square of $x$, and $y = 2.4$ when $x = 4$.

Accepted Answer

A)  $y = 0.15 x ^ { 2 }$ 
B)  $y = 1.72 x ^ { 2 }$ 
C)  $y = 0.2 x ^ { 2 }$ 
D)  $y = 0.19 \sqrt { x }$ 
A)  $y = 0.15 x ^ { 2 }$ 
B)  $y = 1.72 x ^ { 2 }$ 
C)  $y = 0.2 x ^ { 2 }$ 
D)  $y = 0.19 \sqrt { x }$

Perform the indicated operation. Simplify, if possible. - $\frac { - 16 x } { 5 ( 4 x + 1 ) } + \frac { 1 } { 5 x ( 4 x + 1 ) } - \frac { 5 } { x }$

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

Add. Simplify, if possible. - $\frac { 2 } { 15 x } + \frac { 4 } { 21 x ^ { 2 } }$

Find an equation of variation in which the following are true. - $y$ varies directly as $x$ and inversely as $z$ , and $y = 18$ when $x = 2$ and $z = 9$ .

Solve the equation. - $\frac { x - 2 } { x + 4 } = \frac { 1 } { 5 }$

Find an equation of variation in which the following are true. - $y$ varies directly as the square of $x$ , and $y = 2.4$ when $x = 4$ .

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

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Radical Expressions, Equations, and Functions

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Exam 6: Rational Expressions and Equations

Perform the indicated operation. Simplify, if possible. - −16x5(4x+1)+15x(4x+1)−5x\frac { - 16 x } { 5 ( 4 x + 1 ) } + \frac { 1 } { 5 x ( 4 x + 1 ) } - \frac { 5 } { x }5(4x+1)−16x​+5x(4x+1)1​−x5​

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

Add. Simplify, if possible. - 215x+421x2\frac { 2 } { 15 x } + \frac { 4 } { 21 x ^ { 2 } }15x2​+21x24​

Find an equation of variation in which the following are true. - yyy varies directly as xxx and inversely as zzz , and y=18y = 18y=18 when x=2x = 2x=2 and z=9z = 9z=9 .

Solve the equation. - x−2x+4=15\frac { x - 2 } { x + 4 } = \frac { 1 } { 5 }x+4x−2​=51​

Find an equation of variation in which the following are true. - yyy varies directly as the square of xxx , and y=2.4y = 2.4y=2.4 when x=4x = 4x=4 .