Question 1

Perform the operations and simplify the result when possible. $\frac { 5 } { x ^ { 2 } - 3 x - 4 } - \frac { x } { 3 x ^ { 2 } - 10 x - 8 }$

Accepted Answer

A)  $\frac { - x ^ { 2 } + 14 x + 10 } { ( x - 4 ) ( x + 1 ) ( 3 x + 2 ) }$ 
B)  $\frac { x ^ { 2 } + 14 x + 10 } { ( x - 3 ) ( x + 1 ) ( 3 x + 2 ) }$ 
C)  $\frac { - x ^ { 2 } + 14 x + 10 } { ( x - 4 ) ( x + 1 ) \left( 3 x ^ { 2 } - 7 x - 6 \right) }$ 
D)  $\frac { - x ^ { 2 } + 14 x + 10 } { ( x + 1 ) ( 3 x + 2 ) }$ 
E)  $\frac { - x ^ { 2 } + 10 x + 10 } { ( x - 4 ) ( x + 1 ) ( 3 x + 2 ) }$ 
A)  $\frac { - x ^ { 2 } + 14 x + 10 } { ( x - 4 ) ( x + 1 ) ( 3 x + 2 ) }$ 
B)  $\frac { x ^ { 2 } + 14 x + 10 } { ( x - 3 ) ( x + 1 ) ( 3 x + 2 ) }$ 
C)  $\frac { - x ^ { 2 } + 14 x + 10 } { ( x - 4 ) ( x + 1 ) \left( 3 x ^ { 2 } - 7 x - 6 \right) }$ 
D)  $\frac { - x ^ { 2 } + 14 x + 10 } { ( x + 1 ) ( 3 x + 2 ) }$ 
E)  $\frac { - x ^ { 2 } + 10 x + 10 } { ( x - 4 ) ( x + 1 ) ( 3 x + 2 ) }$

Question 2

Divide using long division: $\frac { 8 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 10 } { 2 x - 3 }$

Accepted Answer

A)  $4 x ^ { 2 } - 5 x - 6 - \frac { 38 } { 2 x - 3 }$ 
B)  $4 x ^ { 2 } + 5 x + 9 + \frac { 17 } { 2 x - 3 }$ 
C)  $4 x ^ { 2 } + 5 x - 6 - \frac { 38 } { 2 x - 3 }$ 
D)  $4 x ^ { 2 } + 5 x + 9 - \frac { 27 } { 2 x - 3 }$ 
A)  $4 x ^ { 2 } - 5 x - 6 - \frac { 38 } { 2 x - 3 }$ 
B)  $4 x ^ { 2 } + 5 x + 9 + \frac { 17 } { 2 x - 3 }$ 
C)  $4 x ^ { 2 } + 5 x - 6 - \frac { 38 } { 2 x - 3 }$ 
D)  $4 x ^ { 2 } + 5 x + 9 - \frac { 27 } { 2 x - 3 }$

Question 3

A homeowner estimates that it will take her 9 days to roof her house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer?
 __________ days

Accepted Answer

The answer of A homeowner estimates that it will take...

Question 4

Perform the operations and simplify the result when possible. $\frac { 9 } { x + 1 } - \frac { 6 } { x - 1 } + \frac { x + 11 } { x ^ { 2 } - 1 }$

Accepted Answer

The answer of Perform the operations and simplify the result...

Question 5

Add, and then simplify, if possible. $\frac { 5 x } { 3 x - 9 } + \frac { x - 18 } { 3 x - 9 }$

Accepted Answer

The answer of Add, and then simplify, if possible. \(\frac...

Question 6

A man roller-blades at a rate 6 miles per hour faster than he jogs. In the same time it takes him to roller-blade 5 miles he can jog 2 miles. How fast does he jog?
 __________ mph

Accepted Answer

The answer of A man roller-blades at a rate 6...

Question 7

Out of a sample of 250 women's blouses, 10 were rejected because of a missing button. How many blouses would you expect to have a missing button in a run of 600 shirts?

Accepted Answer

A)  15 
B)  24 
C)  20 
D)  25 
A)  15 
B)  24 
C)  20 
D)  25

Question 8

Add, and then simplify, if possible. $\frac { 5 x } { 2 x + 2 } + \frac { 7 x + 12 } { 2 x + 2 }$

Accepted Answer

A)  6 
B)  7 
C)  3 
D)  4 x 
E)  6 x 
A)  6 
B)  7 
C)  3 
D)  4 x 
E)  6 x

Question 9

When solving a rational equation, if we obtain a number that does not satisfy the original equation, the number is called a(n) __________ solution.

Accepted Answer

The answer of When solving a rational equation, if we...

Question 10

Perform the indicated operation. Simplify, if possible. $\frac { 4 } { a + 6 } - \frac { 3 } { a }$

Accepted Answer

A)  $\frac { 1 } { a ( a + 6 ) }$ 
B)  $\frac { 13 } { a ( a + 6 ) }$ 
C)  $\frac { a + 6 } { a ( a + 6 ) }$ 
D)  $\frac { a - 18 } { a ( a + 6 ) }$ 
A)  $\frac { 1 } { a ( a + 6 ) }$ 
B)  $\frac { 13 } { a ( a + 6 ) }$ 
C)  $\frac { a + 6 } { a ( a + 6 ) }$ 
D)  $\frac { a - 18 } { a ( a + 6 ) }$

Question 11

A recipe for guacamole dip calls for 5 avocados. If they are advertised at 3 for $1.89, what will 5 avocados cost?

Accepted Answer

A)  $2.90 
B)  $3.90 
C)  $3.65 
D)  $3.40 
E)  $3.15 
A)  $2.90 
B)  $3.90 
C)  $3.65 
D)  $3.40 
E)  $3.15

Question 12

Solve the problem by writing a variation model. The costs of a trucking company vary jointly as the number of trucks in service and the number of hours they are used. When 3 trucks are used for 7 hours each, the costs are $1,533. Find the costs of using 10 trucks, each for 13 hours. $ __________

Accepted Answer

The answer of Solve the problem by writing a variation...

Question 13

Solve the proportion, if possible. $\frac { n ^ { 2 } } { 4 } = \frac { n } { n + 3 }$

Accepted Answer

The answer of Solve the proportion, if possible. \(\frac {...

Question 14

Write the expression " R varies directly with the square of x " in symbols.

Accepted Answer

A)  $R = k \sqrt { x }$ 
B)  $R = \frac { k } { \sqrt { x } }$ 
C)  $R = k x ^ { 2 }$ 
D)  $R = \frac { k } { x ^ { 2 } }$ 
A)  $R = k \sqrt { x }$ 
B)  $R = \frac { k } { \sqrt { x } }$ 
C)  $R = k x ^ { 2 }$ 
D)  $R = \frac { k } { x ^ { 2 } }$

Question 15

Perform the division. $\frac { 9 x ^ { 8 } y ^ { 7 } + 18 x ^ { 6 } y - 27 x y ^ { 8 } } { - 9 x ^ { 7 } y ^ { 7 } }$

Accepted Answer

A)  $- x - \frac { 2 } { x y ^ { 6 } } + \frac { 3 y } { x ^ { 7 } }$ 
B)  $x + \frac { 2 } { x y ^ { 6 } } - \frac { 3 y } { x ^ { 6 } }$ 
C)  $- x - \frac { 2 } { x y ^ { 6 } } - \frac { 3 y } { x ^ { 6 } }$ 
D)  $- x - \frac { 2 } { x y ^ { 6 } } + \frac { 3 y } { x ^ { 6 } }$ 
E)  $- x - \frac { 2 } { x y ^ { 7 } } + \frac { 3 y } { x ^ { 6 } }$ 
A)  $- x - \frac { 2 } { x y ^ { 6 } } + \frac { 3 y } { x ^ { 7 } }$ 
B)  $x + \frac { 2 } { x y ^ { 6 } } - \frac { 3 y } { x ^ { 6 } }$ 
C)  $- x - \frac { 2 } { x y ^ { 6 } } - \frac { 3 y } { x ^ { 6 } }$ 
D)  $- x - \frac { 2 } { x y ^ { 6 } } + \frac { 3 y } { x ^ { 6 } }$ 
E)  $- x - \frac { 2 } { x y ^ { 7 } } + \frac { 3 y } { x ^ { 6 } }$

Question 16

Solve the formula for the indicated variable. $\frac { p } { m } = q t$ for $P$

Accepted Answer

The answer of Solve the formula for the indicated variable....

Question 17

Shane can drive a motorboat 30 miles down a river in the same amount of time that he can drive 20 miles upstream. Find the speed of the current if the speed of the boat is 15 mph in still water. ______ mph

Accepted Answer

The answer of Shane can drive a motorboat 30 miles...

Question 18

Use synthetic division to perform the division. $\frac { 4 x ^ { 3 } - 21 x ^ { 2 } + 11 x - 30 } { x - 5 }$

Accepted Answer

The answer of Use synthetic division to perform the division....

Question 19

An equation that states that two ratios are equal, such as $\frac { 1 } { 2 } = \frac { 2 } { 4 }$ , is called a __________.

Accepted Answer

The answer of An equation that states that two ratios...

Question 20

Solve $d = \frac { 4 c b } { b + c }$ for b.

Accepted Answer

A)  $b = \frac { c d } { 4 c - 1 }$ 
B)  $b = \frac { 1 } { 4 }$ 
C)  $b = \frac { d ( b + c ) } { 4 c }$ 
D)  $b = \frac { c d } { 4 c - d }$ 
A)  $b = \frac { c d } { 4 c - 1 }$ 
B)  $b = \frac { 1 } { 4 }$ 
C)  $b = \frac { d ( b + c ) } { 4 c }$ 
D)  $b = \frac { c d } { 4 c - d }$

Perform the operations and simplify the result when possible. $\frac { 5 } { x ^ { 2 } - 3 x - 4 } - \frac { x } { 3 x ^ { 2 } - 10 x - 8 }$

Divide using long division: $\frac { 8 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 10 } { 2 x - 3 }$

A homeowner estimates that it will take her 9 days to roof her house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer? __________ days

Perform the operations and simplify the result when possible. $\frac { 9 } { x + 1 } - \frac { 6 } { x - 1 } + \frac { x + 11 } { x ^ { 2 } - 1 }$

Add, and then simplify, if possible. $\frac { 5 x } { 3 x - 9 } + \frac { x - 18 } { 3 x - 9 }$

A man roller-blades at a rate 6 miles per hour faster than he jogs. In the same time it takes him to roller-blade 5 miles he can jog 2 miles. How fast does he jog? __________ mph

Out of a sample of 250 women's blouses, 10 were rejected because of a missing button. How many blouses would you expect to have a missing button in a run of 600 shirts?

Add, and then simplify, if possible. $\frac { 5 x } { 2 x + 2 } + \frac { 7 x + 12 } { 2 x + 2 }$

When solving a rational equation, if we obtain a number that does not satisfy the original equation, the number is called a(n) __________ solution.

Perform the indicated operation. Simplify, if possible. $\frac { 4 } { a + 6 } - \frac { 3 } { a }$

A recipe for guacamole dip calls for 5 avocados. If they are advertised at 3 for $1.89, what will 5 avocados cost?

Solve the problem by writing a variation model. The costs of a trucking company vary jointly as the number of trucks in service and the number of hours they are used. When 3 trucks are used for 7 hours each, the costs are $1,533. Find the costs of using 10 trucks, each for 13 hours. $ __________

Solve the proportion, if possible. $\frac { n ^ { 2 } } { 4 } = \frac { n } { n + 3 }$

Write the expression " R varies directly with the square of x " in symbols.

Perform the division. $\frac { 9 x ^ { 8 } y ^ { 7 } + 18 x ^ { 6 } y - 27 x y ^ { 8 } } { - 9 x ^ { 7 } y ^ { 7 } }$

Solve the formula for the indicated variable. $\frac { p } { m } = q t$ for $P$

Shane can drive a motorboat 30 miles down a river in the same amount of time that he can drive 20 miles upstream. Find the speed of the current if the speed of the boat is 15 mph in still water. ______ mph

Use synthetic division to perform the division. $\frac { 4 x ^ { 3 } - 21 x ^ { 2 } + 11 x - 30 } { x - 5 }$

An equation that states that two ratios are equal, such as $\frac { 1 } { 2 } = \frac { 2 } { 4 }$ , is called a __________.

Solve $d = \frac { 4 c b } { b + c }$ for b.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 6: Rational Expression and Equations

Perform the operations and simplify the result when possible. 5x2−3x−4−x3x2−10x−8\frac { 5 } { x ^ { 2 } - 3 x - 4 } - \frac { x } { 3 x ^ { 2 } - 10 x - 8 }x2−3x−45​−3x2−10x−8x​

Divide using long division: 8x3−2x2+3x−102x−3\frac { 8 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 10 } { 2 x - 3 }2x−38x3−2x2+3x−10​

A homeowner estimates that it will take her 9 days to roof her house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer? __________ days

Perform the operations and simplify the result when possible. 9x+1−6x−1+x+11x2−1\frac { 9 } { x + 1 } - \frac { 6 } { x - 1 } + \frac { x + 11 } { x ^ { 2 } - 1 }x+19​−x−16​+x2−1x+11​

Add, and then simplify, if possible. 5x3x−9+x−183x−9\frac { 5 x } { 3 x - 9 } + \frac { x - 18 } { 3 x - 9 }3x−95x​+3x−9x−18​

A man roller-blades at a rate 6 miles per hour faster than he jogs. In the same time it takes him to roller-blade 5 miles he can jog 2 miles. How fast does he jog? __________ mph

Out of a sample of 250 women's blouses, 10 were rejected because of a missing button. How many blouses would you expect to have a missing button in a run of 600 shirts?

Add, and then simplify, if possible. 5x2x+2+7x+122x+2\frac { 5 x } { 2 x + 2 } + \frac { 7 x + 12 } { 2 x + 2 }2x+25x​+2x+27x+12​

When solving a rational equation, if we obtain a number that does not satisfy the original equation, the number is called a(n) __________ solution.

Perform the indicated operation. Simplify, if possible. 4a+6−3a\frac { 4 } { a + 6 } - \frac { 3 } { a }a+64​−a3​

A recipe for guacamole dip calls for 5 avocados. If they are advertised at 3 for $1.89, what will 5 avocados cost?

Solve the problem by writing a variation model. The costs of a trucking company vary jointly as the number of trucks in service and the number of hours they are used. When 3 trucks are used for 7 hours each, the costs are $1,533. Find the costs of using 10 trucks, each for 13 hours. $ __________

Solve the proportion, if possible. n24=nn+3\frac { n ^ { 2 } } { 4 } = \frac { n } { n + 3 }4n2​=n+3n​

Write the expression " R varies directly with the square of x " in symbols.

Perform the division. 9x8y7+18x6y−27xy8−9x7y7\frac { 9 x ^ { 8 } y ^ { 7 } + 18 x ^ { 6 } y - 27 x y ^ { 8 } } { - 9 x ^ { 7 } y ^ { 7 } }−9x7y79x8y7+18x6y−27xy8​

Solve the formula for the indicated variable. pm=qt\frac { p } { m } = q tmp​=qt for PPP

Shane can drive a motorboat 30 miles down a river in the same amount of time that he can drive 20 miles upstream. Find the speed of the current if the speed of the boat is 15 mph in still water. ______ mph

Use synthetic division to perform the division. 4x3−21x2+11x−30x−5\frac { 4 x ^ { 3 } - 21 x ^ { 2 } + 11 x - 30 } { x - 5 }x−54x3−21x2+11x−30​

An equation that states that two ratios are equal, such as 12=24\frac { 1 } { 2 } = \frac { 2 } { 4 }21​=42​ , is called a __________.

Solve d=4cbb+cd = \frac { 4 c b } { b + c }d=b+c4cb​ for b.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Perform the operations and simplify the result when possible. $\frac { 5 } { x ^ { 2 } - 3 x - 4 } - \frac { x } { 3 x ^ { 2 } - 10 x - 8 }$

Divide using long division: $\frac { 8 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 10 } { 2 x - 3 }$

Perform the operations and simplify the result when possible. $\frac { 9 } { x + 1 } - \frac { 6 } { x - 1 } + \frac { x + 11 } { x ^ { 2 } - 1 }$

Add, and then simplify, if possible. $\frac { 5 x } { 3 x - 9 } + \frac { x - 18 } { 3 x - 9 }$

Add, and then simplify, if possible. $\frac { 5 x } { 2 x + 2 } + \frac { 7 x + 12 } { 2 x + 2 }$

Perform the indicated operation. Simplify, if possible. $\frac { 4 } { a + 6 } - \frac { 3 } { a }$

Solve the proportion, if possible. $\frac { n ^ { 2 } } { 4 } = \frac { n } { n + 3 }$

Perform the division. $\frac { 9 x ^ { 8 } y ^ { 7 } + 18 x ^ { 6 } y - 27 x y ^ { 8 } } { - 9 x ^ { 7 } y ^ { 7 } }$

Solve the formula for the indicated variable. $\frac { p } { m } = q t$ for $P$

Use synthetic division to perform the division. $\frac { 4 x ^ { 3 } - 21 x ^ { 2 } + 11 x - 30 } { x - 5 }$

An equation that states that two ratios are equal, such as $\frac { 1 } { 2 } = \frac { 2 } { 4 }$ , is called a __________.

Solve $d = \frac { 4 c b } { b + c }$ for b.