Question 1

Find all numbers for which the rational expression is not defined.
-$$\frac { \mathrm { d } - 7 } { 4 - \mathrm { d } }$$

Accepted Answer

A) d = 4 
B) d = -4 
C) d = 4, 7 
D) None 
A) d = 4 
B) d = -4 
C) d = 4, 7 
D) None

Question 2

Simplify.
-$$\frac { y ^ { 2 } + 5 y - 24 } { y ^ { 2 } + 4 y - 32 }$$

Accepted Answer

A)  $- \frac { y ^ { 2 } + 5 y - 24 } { y ^ { 2 } + 4 y - 32 }$ 
B)  $\frac { 5 y - 24 } { 4 y - 32 }$ 
C)  $\frac { y - 3 } { y - 4 }$ 
D)  $\frac { 5 y - 3 } { 4 y - 4 }$ 
A)  $- \frac { y ^ { 2 } + 5 y - 24 } { y ^ { 2 } + 4 y - 32 }$ 
B)  $\frac { 5 y - 24 } { 4 y - 32 }$ 
C)  $\frac { y - 3 } { y - 4 }$ 
D)  $\frac { 5 y - 3 } { 4 y - 4 }$

Question 3

Find an equation of variation in which the following are true.
-$y$ varies jointly as $x$ and $w$ and inversely as $z$, and $y = \frac { 9 } { 2 }$ when $x = 2 , w = 6$, and $z = 24$.

Accepted Answer

A)  $y = \frac { 6 z } { x w }$ 
B)  $y = 4 x w z$ 
C)  $y = \frac { 6 x w } { z ^ { 2 } }$ 
D)  $y = \frac { 9 x w } { z }$ 
A)  $y = \frac { 6 z } { x w }$ 
B)  $y = 4 x w z$ 
C)  $y = \frac { 6 x w } { z ^ { 2 } }$ 
D)  $y = \frac { 9 x w } { z }$

Question 4

Multiply and, if possible, simplify.
-$$\frac { k ^ { 2 } + 6 k + 8 } { k ^ { 2 } + 8 k + 12 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } + 8 k + 16 }$$

Accepted Answer

A)  $\frac { k ^ { 2 } + 6 k } { k + 4 }$ 
B)  $\frac { 1 } { \mathrm { k } + 4 }$ 
C)  $\frac { \mathrm { k } } { \mathrm { k } ^ { 2 } + 8 \mathrm { k } + 12 }$ 
D)  $\frac { \mathrm { k } } { \mathrm { k } + 4 }$ 
A)  $\frac { k ^ { 2 } + 6 k } { k + 4 }$ 
B)  $\frac { 1 } { \mathrm { k } + 4 }$ 
C)  $\frac { \mathrm { k } } { \mathrm { k } ^ { 2 } + 8 \mathrm { k } + 12 }$ 
D)  $\frac { \mathrm { k } } { \mathrm { k } + 4 }$

Question 5

Divide and simplify.
-$\frac { 5 } { 9 } \div \frac { 6 } { 5 }$

Accepted Answer

A)  $\frac { 25 } { 54 }$ 
B)  $\frac { 54 } { 25 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 3 } { 2 }$ 
A)  $\frac { 25 } { 54 }$ 
B)  $\frac { 54 } { 25 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 3 } { 2 }$

Question 6

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

Accepted Answer

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

Question 7

Solve the problem.
-A quality-control inspector examined 290 calculators and found 14 of them to be defective. At this rate, how many defective calculators will there be in a batch of 27,840 calculators?

Accepted Answer

A) 96 
B) 4060 
C) 7 
D) 1344 
A) 96 
B) 4060 
C) 7 
D) 1344

Question 8

Find a linear function whose graph has the given slope and y-intercept.
-$\frac { b - 7 } { 7 b - 28 }$

Accepted Answer

A)  $b = - 7$ 
B)  $b = 28$ 
C)  $b = 4$ 
D)  $b = 0$ 
A)  $b = - 7$ 
B)  $b = 28$ 
C)  $b = 4$ 
D)  $b = 0$

Question 9

Find the LCM.
-$x ^ { 2 } - 9 x + 20 , x ^ { 2 } - 3 x - 4$

Accepted Answer

A)  $( x - 4 ) ( x + 1 )$ 
B)  $( x - 5 ) ( x - 4 )$ 
C)  $( x - 5 ) ( x - 4 ) ( x + 1 )$ 
D)  $( x + 5 ) ( x + 4 ) ( x + 1 )$ 
A)  $( x - 4 ) ( x + 1 )$ 
B)  $( x - 5 ) ( x - 4 )$ 
C)  $( x - 5 ) ( x - 4 ) ( x + 1 )$ 
D)  $( x + 5 ) ( x + 4 ) ( x + 1 )$

Question 10

Solve the equation.
-$$\frac { 1 } { x + 6 } = \frac { 2 } { x - 1 }$$

Accepted Answer

A)  $- 7$ 
B)  $- 13$ 
C)  $\frac { 13 } { 3 }$ 
D)  $- 11$ 
A)  $- 7$ 
B)  $- 13$ 
C)  $\frac { 13 } { 3 }$ 
D)  $- 11$

Question 11

Perform the indicated operation. Simplify, if possible.
-$$\frac { 5 ( y - 1 ) } { 5 y - 4 } - \frac { y - 5 } { 4 - 5 y } - \frac { 6 y } { 5 y - 4 }$$

Accepted Answer

A)  $\frac { 10 } { 5 y - 4 }$ 
B)  $\frac { - 10 } { 5 y - 4 }$ 
C)  $\frac { - 2 y } { 5 y - 4 }$ 
D)  $\frac { - 10 } { ( 5 y - 4 ) ( 4 - 5 y ) }$ 
A)  $\frac { 10 } { 5 y - 4 }$ 
B)  $\frac { - 10 } { 5 y - 4 }$ 
C)  $\frac { - 2 y } { 5 y - 4 }$ 
D)  $\frac { - 10 } { ( 5 y - 4 ) ( 4 - 5 y ) }$

Question 12

Solve the equation.
-$$\frac { x - 6 } { x - 4 } = \frac { 7 } { 4 - x }$$

Accepted Answer

A)  13 
B)  1 
C)  $- 1$ 
D)  $- 13$ 
A)  13 
B)  1 
C)  $- 1$ 
D)  $- 13$

Question 13

Divide and simplify.
-$$\frac { 45 } { y - x } \div \frac { 9 } { x - y }$$

Accepted Answer

A)  $\frac { 5 ( x - y ) } { y - x }$ 
B)  $- 45$ 
C)  5 
D)  $- 5$ 
A)  $\frac { 5 ( x - y ) } { y - x }$ 
B)  $- 45$ 
C)  5 
D)  $- 5$

Question 14

Divide and simplify.
-$$\frac { z ^ { 2 } + 6 z + 8 } { z ^ { 2 } + 10 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 13 z + 42 }$$

Accepted Answer

A)  $\frac { z } { z ^ { 2 } + 10 z + 24 }$ 
B)  $z + 7$ 
C)  $\frac { \mathrm { z } + 7 } { \mathrm { z } }$ 
D)  $\frac { z + 7 } { z ^ { 2 } + 6 z }$ 
A)  $\frac { z } { z ^ { 2 } + 10 z + 24 }$ 
B)  $z + 7$ 
C)  $\frac { \mathrm { z } + 7 } { \mathrm { z } }$ 
D)  $\frac { z + 7 } { z ^ { 2 } + 6 z }$

Question 15

Solve.
-Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity v. If a car traveling at a speed of 40 mph with a surface area of $37 \mathrm { ft } ^ { 2 }$ experiences a drag of $236.8 \mathrm {~N}$ (Newtons), how fast must a car with $48 \mathrm { ft } ^ { 2 }$ of surface area travel in order to

Accepted Answer

A) 66 mph 
B) 69 mph 
C) 71 mph 
D) 74 mph 
A) 66 mph 
B) 69 mph 
C) 71 mph 
D) 74 mph

Question 16

Solve.
-At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the square of its diameter d. If the resistance is 0.4 ohm when the diameter is 1 mm and the length is 200 cm, what is the
Resistance when the diameter is 2 mm and the length is 1620 cm?

Accepted Answer

A) 1.62 ohm 
B) 162 ohm 
C) 0.81 ohm 
D) 405 ohm 
A) 1.62 ohm 
B) 162 ohm 
C) 0.81 ohm 
D) 405 ohm

Question 17

Find an equation of variation in which the following are true.
-$y$ varies jointly as $x$ and $z$ and inversely as the product of $w$ and $p$, and $y = \frac { 45 } { 80 }$ when $x = 5 , z = 9 , w = 8$, and $\mathrm { p } = 5 .$

Accepted Answer

A)  $y = \frac { 2 x z } { w p }$ 
B)  $y = \frac { w p } { 2 x z }$ 
C)  $y = \frac { 2 w p } { x z }$ 
D)  $y = \frac { x z } { 2 w p }$ 
A)  $y = \frac { 2 x z } { w p }$ 
B)  $y = \frac { w p } { 2 x z }$ 
C)  $y = \frac { 2 w p } { x z }$ 
D)  $y = \frac { x z } { 2 w p }$

Question 18

Subtract. Simplify, if possible.
-$$\frac { 5 x } { x ^ { 2 } - 9 } - \frac { x } { x - 3 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } + 8 x } { x ^ { 2 } - 9 }$ 
B)  $\frac { x ^ { 2 } + 2 x } { x ^ { 2 } - 9 }$ 
C)  $\frac { - x ^ { 2 } + 8 x } { x ^ { 2 } - 9 }$ 
D)  $\frac { - x ^ { 2 } + 2 x } { x ^ { 2 } - 9 }$ 
A)  $\frac { x ^ { 2 } + 8 x } { x ^ { 2 } - 9 }$ 
B)  $\frac { x ^ { 2 } + 2 x } { x ^ { 2 } - 9 }$ 
C)  $\frac { - x ^ { 2 } + 8 x } { x ^ { 2 } - 9 }$ 
D)  $\frac { - x ^ { 2 } + 2 x } { x ^ { 2 } - 9 }$

Question 19

Solve the equation.
-$$\frac { 5 } { 10 - x } = \frac { 5 - x } { x - 10 }$$

Accepted Answer

A)  No solution 
B)  0 
C)  5 
D)  10 
A)  No solution 
B)  0 
C)  5 
D)  10

Question 20

Add. Simplify, if possible.
-$\frac { 2 } { x ^ { 6 } y } + \frac { 9 } { x y ^ { 5 } }$

Accepted Answer

A)  $\frac { 9 x ^ { 5 } + 2 y ^ { 4 } } { x ^ { 6 } y ^ { 5 } }$ 
B)  $\frac { 9 x ^ { 6 } + 2 y ^ { 5 } } { x ^ { 6 } y ^ { 5 } }$ 
C)  $\frac { 11 } { x ^ { 6 } y ^ { 5 } }$ 
D)  $\frac { 11 } { x y }$ 
A)  $\frac { 9 x ^ { 5 } + 2 y ^ { 4 } } { x ^ { 6 } y ^ { 5 } }$ 
B)  $\frac { 9 x ^ { 6 } + 2 y ^ { 5 } } { x ^ { 6 } y ^ { 5 } }$ 
C)  $\frac { 11 } { x ^ { 6 } y ^ { 5 } }$ 
D)  $\frac { 11 } { x y }$

Find all numbers for which the rational expression is not defined. - $\frac { \mathrm { d } - 7 } { 4 - \mathrm { d } }$

Simplify. - $\frac { y ^ { 2 } + 5 y - 24 } { y ^ { 2 } + 4 y - 32 }$

Find an equation of variation in which the following are true. - $y$ varies jointly as $x$ and $w$ and inversely as $z$ , and $y = \frac { 9 } { 2 }$ when $x = 2 , w = 6$ , and $z = 24$ .

Multiply and, if possible, simplify. - $\frac { k ^ { 2 } + 6 k + 8 } { k ^ { 2 } + 8 k + 12 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } + 8 k + 16 }$

Divide and simplify. - $\frac { 5 } { 9 } \div \frac { 6 } { 5 }$

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

Solve the problem. -A quality-control inspector examined 290 calculators and found 14 of them to be defective. At this rate, how many defective calculators will there be in a batch of 27,840 calculators?

Find a linear function whose graph has the given slope and y-intercept. - $\frac { b - 7 } { 7 b - 28 }$

Find the LCM. - $x ^ { 2 } - 9 x + 20 , x ^ { 2 } - 3 x - 4$

Solve the equation. - $\frac { 1 } { x + 6 } = \frac { 2 } { x - 1 }$

Perform the indicated operation. Simplify, if possible. - $\frac { 5 ( y - 1 ) } { 5 y - 4 } - \frac { y - 5 } { 4 - 5 y } - \frac { 6 y } { 5 y - 4 }$

Solve the equation. - $\frac { x - 6 } { x - 4 } = \frac { 7 } { 4 - x }$

Divide and simplify. - $\frac { 45 } { y - x } \div \frac { 9 } { x - y }$

Divide and simplify. - $\frac { z ^ { 2 } + 6 z + 8 } { z ^ { 2 } + 10 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 13 z + 42 }$

Solve. -At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the square of its diameter d. If the resistance is 0.4 ohm when the diameter is 1 mm and the length is 200 cm, what is the Resistance when the diameter is 2 mm and the length is 1620 cm?

Find an equation of variation in which the following are true. - $y$ varies jointly as $x$ and $z$ and inversely as the product of $w$ and $p$ , and $y = \frac { 45 } { 80 }$ when $x = 5 , z = 9 , w = 8$ , and $\mathrm { p } = 5 .$

Subtract. Simplify, if possible. - $\frac { 5 x } { x ^ { 2 } - 9 } - \frac { x } { x - 3 }$

Solve the equation. - $\frac { 5 } { 10 - x } = \frac { 5 - x } { x - 10 }$

Add. Simplify, if possible. - $\frac { 2 } { x ^ { 6 } y } + \frac { 9 } { x y ^ { 5 } }$

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

Filters

Exam 6: Rational Expressions and Equations

Find all numbers for which the rational expression is not defined. - d−74−d\frac { \mathrm { d } - 7 } { 4 - \mathrm { d } }4−dd−7​

Simplify. - y2+5y−24y2+4y−32\frac { y ^ { 2 } + 5 y - 24 } { y ^ { 2 } + 4 y - 32 }y2+4y−32y2+5y−24​

Find an equation of variation in which the following are true. - yyy varies jointly as xxx and www and inversely as zzz , and y=92y = \frac { 9 } { 2 }y=29​ when x=2,w=6x = 2 , w = 6x=2,w=6 , and z=24z = 24z=24 .

Multiply and, if possible, simplify. - k2+6k+8k2+8k+12⋅k2+6kk2+8k+16\frac { k ^ { 2 } + 6 k + 8 } { k ^ { 2 } + 8 k + 12 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } + 8 k + 16 }k2+8k+12k2+6k+8​⋅k2+8k+16k2+6k​

Divide and simplify. - 59÷65\frac { 5 } { 9 } \div \frac { 6 } { 5 }95​÷56​

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​