Question 1

Simplify the rational expression. $\frac { 16 x ^ { 2 } y + 32 x y ^ { 2 } - 48 y ^ { 3 } } { 60 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 3 } }$

Accepted Answer

The answer of Simplify the rational expression. \(\frac { 16...

Question 2

A rational expression is the indicated quotient of two expressions.

Accepted Answer

A) True 
 B)False

Question 3

Perform the operation involving rational numbers. $\frac { 13 } { 45 } + \frac { 9 } { 20 }$

Accepted Answer

A)  $\frac { 133 } { 179 }$ 
B)  $\frac { 180 } { 133 }$ 
C)  $\frac { 133 } { 180 }$ 
D)  $\frac { 133 } { 360 }$ 
A)  $\frac { 133 } { 179 }$ 
B)  $\frac { 180 } { 133 }$ 
C)  $\frac { 133 } { 180 }$ 
D)  $\frac { 133 } { 360 }$

Question 4

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 2 x } + \frac { 8 } { x }$

Accepted Answer

A)  $\frac { 15 x + 16 } { x + 2 }$ 
B)  $\frac { 15 x + 16 } { x ( x + 2 ) }$ 
C)  $\frac { 7 x + 16 } { x ( x + 2 ) }$ 
A)  $\frac { 15 x + 16 } { x + 2 }$ 
B)  $\frac { 15 x + 16 } { x ( x + 2 ) }$ 
C)  $\frac { 7 x + 16 } { x ( x + 2 ) }$

Question 5

Solve the equation. $\frac { x } { 6 x - 6 } + \frac { 4 } { x ^ { 2 } - 1 } = \frac { 1 } { 6 }$

Accepted Answer

A)  x = 1 
B)  x = 6 
C)  x = -25 
A)  x = 1 
B)  x = 6 
C)  x = -25

Question 6

Solve the equation. $\frac { 7 } { n + 4 } + \frac { 1 } { n - 5 } = \frac { 7 n - 1 } { n ^ { 2 } - n - 20 }$

Accepted Answer

A)  n = 30 
B)  n = 5 
C)  n = -4 
A)  n = 30 
B)  n = 5 
C)  n = -4

Question 7

Simplify the rational expression. $\frac { n r - 12 - 4 n + 3 r } { n r + 15 + 3 r + 5 n }$

Accepted Answer

A)  $\frac { r + 4 } { r - 5 }$ 
B)  $- \frac { r + 4 } { r + 5 }$ 
C)  $- \frac { r + 3 } { r + 4 }$ 
D)  $\frac { r - 4 } { r + 5 }$ 
A)  $\frac { r + 4 } { r - 5 }$ 
B)  $- \frac { r + 4 } { r + 5 }$ 
C)  $- \frac { r + 3 } { r + 4 }$ 
D)  $\frac { r - 4 } { r + 5 }$

Question 8

Kent drives his Mazda 106 miles in the same time that Dave drives his Nissan 100 miles. If Kent averages 3 miles per hour faster than Dave, find their rates. Kent drives __________ mph Dave drives __________ mph

Accepted Answer

The answer of Kent drives his Mazda 106 miles in...

Question 9

Simplify the rational expression. $\frac { m ^ { 2 } - 81 } { 9 - m }$

Accepted Answer

The answer of Simplify the rational expression. \(\frac { m...

Question 10

Solve the equation. $\frac { 2 y - 17 } { 8 y ^ { 2 } + 8 y - 6 } - \frac { 4 } { 2 y + 3 } = \frac { 5 } { 4 y - 2 }$

Accepted Answer

The answer of Solve the equation. \(\frac { 2 y...

Question 11

Simplify the rational expression. $\frac { 5 x - 7 } { 7 - 5 x }$

Accepted Answer

To simplify the rational expression \fra

Question 12

Perform the indicated operation involving rational expressions. $\frac { n r + 8 n - 8 r - 64 } { n r + 4 n + 4 r + 16 } \cdot \frac { n ^ { 2 } - 16 } { n ^ { 3 } - 8 n ^ { 2 } }$

Accepted Answer

A)  $\frac { n r - 4 r + 8 n + 32 } { m n + 4 n }$ 
B)  $\frac { n r - 4 r + 8 n - 32 } { m ^ { 2 } + 4 n ^ { 2 } }$ 
C)  $\frac { n r + 4 r + 8 n - 32 } { m ^ { 2 } - 4 n ^ { 2 } }$ 
D)  $\frac { n r - 4 r + 8 n + 32 } { r ^ { 2 } + 4 n ^ { 2 } }$ 
A)  $\frac { n r - 4 r + 8 n + 32 } { m n + 4 n }$ 
B)  $\frac { n r - 4 r + 8 n - 32 } { m ^ { 2 } + 4 n ^ { 2 } }$ 
C)  $\frac { n r + 4 r + 8 n - 32 } { m ^ { 2 } - 4 n ^ { 2 } }$ 
D)  $\frac { n r - 4 r + 8 n + 32 } { r ^ { 2 } + 4 n ^ { 2 } }$

Question 13

Solve the equation. $\frac { n } { 77 - n } = 5 + \frac { 5 } { 77 - n }$

Accepted Answer

The answer of Solve the equation. \(\frac { n }...

Question 14

Solve the equation. $\frac { 5 } { n } + \frac { 1 } { 12 } = \frac { 41 } { 6 n }$

Accepted Answer

A)  n = 22 
B)  n = 20 
C)  n = 27 
D)  n = 26 
E)  n = 23 
A)  n = 22 
B)  n = 20 
C)  n = 27 
D)  n = 26 
E)  n = 23

Question 15

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { x - 5 } { 3 } + \frac { x + 8 } { 4 }$

Accepted Answer

The answer of Add the rational expressions. Be sure to...

Question 16

Perform the indicated operations involving rational numbers. Express the final answer in reduced form. $\frac { 2 } { 9 } \cdot \frac { 6 } { 13 } \div \frac { 1 } { 9 }$

Accepted Answer

The answer of Perform the indicated operations involving rational numbers....

Question 17

It takes Amy twice as long to deliver papers as it does Nancy. How long, in minutes, would it take each girl to deliver the papers by herself if they can deliver the papers together in 60 minutes? __________ minutes for Amy __________ minutes for Nancy

Accepted Answer

The answer of It takes Amy twice as long to...

Question 18

Perform the indicated operation and express your answer in simplest form. $$\frac { 2 x + 6 } { x ^ { 2 } + 12 x + 35 } + \frac { 4 x + 5 } { x ^ { 2 } + 11 x + 30 } + \frac { 17 } { x + 6 }$$ Please enter your answer as one fraction with the denominator factored completely.

Accepted Answer

The answer of Perform the indicated operation and express your...

Question 19

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { n - 2 } { 6 } - \frac { n - 7 } { 9 }$

Accepted Answer

The answer of Subtract the rational expressions. Be sure to...

Question 20

Simplify the rational expression. $\frac { - 15 x ^ { 3 } y } { - 27 x y ^ { 4 } }$

Accepted Answer

The answer of Simplify the rational expression. \(\frac { -...

Simplify the rational expression. $\frac { 16 x ^ { 2 } y + 32 x y ^ { 2 } - 48 y ^ { 3 } } { 60 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 3 } }$

A rational expression is the indicated quotient of two expressions.

Perform the operation involving rational numbers. $\frac { 13 } { 45 } + \frac { 9 } { 20 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 2 x } + \frac { 8 } { x }$

Solve the equation. $\frac { x } { 6 x - 6 } + \frac { 4 } { x ^ { 2 } - 1 } = \frac { 1 } { 6 }$

Solve the equation. $\frac { 7 } { n + 4 } + \frac { 1 } { n - 5 } = \frac { 7 n - 1 } { n ^ { 2 } - n - 20 }$

Simplify the rational expression. $\frac { n r - 12 - 4 n + 3 r } { n r + 15 + 3 r + 5 n }$

Kent drives his Mazda 106 miles in the same time that Dave drives his Nissan 100 miles. If Kent averages 3 miles per hour faster than Dave, find their rates. Kent drives mph Dave drives mph

Simplify the rational expression. $\frac { m ^ { 2 } - 81 } { 9 - m }$

Solve the equation. $\frac { 2 y - 17 } { 8 y ^ { 2 } + 8 y - 6 } - \frac { 4 } { 2 y + 3 } = \frac { 5 } { 4 y - 2 }$

Simplify the rational expression. $\frac { 5 x - 7 } { 7 - 5 x }$

Perform the indicated operation involving rational expressions. $\frac { n r + 8 n - 8 r - 64 } { n r + 4 n + 4 r + 16 } \cdot \frac { n ^ { 2 } - 16 } { n ^ { 3 } - 8 n ^ { 2 } }$

Solve the equation. $\frac { n } { 77 - n } = 5 + \frac { 5 } { 77 - n }$

Solve the equation. $\frac { 5 } { n } + \frac { 1 } { 12 } = \frac { 41 } { 6 n }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { x - 5 } { 3 } + \frac { x + 8 } { 4 }$

Perform the indicated operations involving rational numbers. Express the final answer in reduced form. $\frac { 2 } { 9 } \cdot \frac { 6 } { 13 } \div \frac { 1 } { 9 }$

It takes Amy twice as long to deliver papers as it does Nancy. How long, in minutes, would it take each girl to deliver the papers by herself if they can deliver the papers together in 60 minutes? minutes for Amy minutes for Nancy

Perform the indicated operation and express your answer in simplest form. $\frac { 2 x + 6 } { x ^ { 2 } + 12 x + 35 } + \frac { 4 x + 5 } { x ^ { 2 } + 11 x + 30 } + \frac { 17 } { x + 6 }$ Please enter your answer as one fraction with the denominator factored completely.

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { n - 2 } { 6 } - \frac { n - 7 } { 9 }$

Simplify the rational expression. $\frac { - 15 x ^ { 3 } y } { - 27 x y ^ { 4 } }$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 9: Rational Expressions

Simplify the rational expression. 16x2y+32xy2−48y360x3y−40x2y2−20xy3\frac { 16 x ^ { 2 } y + 32 x y ^ { 2 } - 48 y ^ { 3 } } { 60 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 3 } }60x3y−40x2y2−20xy316x2y+32xy2−48y3​

A rational expression is the indicated quotient of two expressions.

Perform the operation involving rational numbers. 1345+920\frac { 13 } { 45 } + \frac { 9 } { 20 }4513​+209​

Perform the indicated operation and express your answer in simplest form. 7xx2+2x+8x\frac { 7 x } { x ^ { 2 } + 2 x } + \frac { 8 } { x }x2+2x7x​+x8​

Solve the equation. x6x−6+4x2−1=16\frac { x } { 6 x - 6 } + \frac { 4 } { x ^ { 2 } - 1 } = \frac { 1 } { 6 }6x−6x​+x2−14​=61​

Solve the equation. 7n+4+1n−5=7n−1n2−n−20\frac { 7 } { n + 4 } + \frac { 1 } { n - 5 } = \frac { 7 n - 1 } { n ^ { 2 } - n - 20 }n+47​+n−51​=n2−n−207n−1​

Simplify the rational expression. nr−12−4n+3rnr+15+3r+5n\frac { n r - 12 - 4 n + 3 r } { n r + 15 + 3 r + 5 n }nr+15+3r+5nnr−12−4n+3r​

Kent drives his Mazda 106 miles in the same time that Dave drives his Nissan 100 miles. If Kent averages 3 miles per hour faster than Dave, find their rates. Kent drives __________ mph Dave drives __________ mph

Simplify the rational expression. m2−819−m\frac { m ^ { 2 } - 81 } { 9 - m }9−mm2−81​

Solve the equation. 2y−178y2+8y−6−42y+3=54y−2\frac { 2 y - 17 } { 8 y ^ { 2 } + 8 y - 6 } - \frac { 4 } { 2 y + 3 } = \frac { 5 } { 4 y - 2 }8y2+8y−62y−17​−2y+34​=4y−25​

Simplify the rational expression. 5x−77−5x\frac { 5 x - 7 } { 7 - 5 x }7−5x5x−7​

Perform the indicated operation involving rational expressions. nr+8n−8r−64nr+4n+4r+16⋅n2−16n3−8n2\frac { n r + 8 n - 8 r - 64 } { n r + 4 n + 4 r + 16 } \cdot \frac { n ^ { 2 } - 16 } { n ^ { 3 } - 8 n ^ { 2 } }nr+4n+4r+16nr+8n−8r−64​⋅n3−8n2n2−16​

Solve the equation. n77−n=5+577−n\frac { n } { 77 - n } = 5 + \frac { 5 } { 77 - n }77−nn​=5+77−n5​

Solve the equation. 5n+112=416n\frac { 5 } { n } + \frac { 1 } { 12 } = \frac { 41 } { 6 n }n5​+121​=6n41​

Add the rational expressions. Be sure to express your answer in simplest form. x−53+x+84\frac { x - 5 } { 3 } + \frac { x + 8 } { 4 }3x−5​+4x+8​

Perform the indicated operations involving rational numbers. Express the final answer in reduced form. 29⋅613÷19\frac { 2 } { 9 } \cdot \frac { 6 } { 13 } \div \frac { 1 } { 9 }92​⋅136​÷91​

It takes Amy twice as long to deliver papers as it does Nancy. How long, in minutes, would it take each girl to deliver the papers by herself if they can deliver the papers together in 60 minutes? __________ minutes for Amy __________ minutes for Nancy

Subtract the rational expressions. Be sure to express your answer in simplest form. n−26−n−79\frac { n - 2 } { 6 } - \frac { n - 7 } { 9 }6n−2​−9n−7​

Simplify the rational expression. −15x3y−27xy4\frac { - 15 x ^ { 3 } y } { - 27 x y ^ { 4 } }−27xy4−15x3y​

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Simplify the rational expression. $\frac { 16 x ^ { 2 } y + 32 x y ^ { 2 } - 48 y ^ { 3 } } { 60 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 3 } }$

Perform the operation involving rational numbers. $\frac { 13 } { 45 } + \frac { 9 } { 20 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 2 x } + \frac { 8 } { x }$

Solve the equation. $\frac { x } { 6 x - 6 } + \frac { 4 } { x ^ { 2 } - 1 } = \frac { 1 } { 6 }$

Solve the equation. $\frac { 7 } { n + 4 } + \frac { 1 } { n - 5 } = \frac { 7 n - 1 } { n ^ { 2 } - n - 20 }$

Simplify the rational expression. $\frac { n r - 12 - 4 n + 3 r } { n r + 15 + 3 r + 5 n }$

Kent drives his Mazda 106 miles in the same time that Dave drives his Nissan 100 miles. If Kent averages 3 miles per hour faster than Dave, find their rates. Kent drives mph Dave drives mph

Simplify the rational expression. $\frac { m ^ { 2 } - 81 } { 9 - m }$

Solve the equation. $\frac { 2 y - 17 } { 8 y ^ { 2 } + 8 y - 6 } - \frac { 4 } { 2 y + 3 } = \frac { 5 } { 4 y - 2 }$

Simplify the rational expression. $\frac { 5 x - 7 } { 7 - 5 x }$

Perform the indicated operation involving rational expressions. $\frac { n r + 8 n - 8 r - 64 } { n r + 4 n + 4 r + 16 } \cdot \frac { n ^ { 2 } - 16 } { n ^ { 3 } - 8 n ^ { 2 } }$

Solve the equation. $\frac { n } { 77 - n } = 5 + \frac { 5 } { 77 - n }$

Solve the equation. $\frac { 5 } { n } + \frac { 1 } { 12 } = \frac { 41 } { 6 n }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { x - 5 } { 3 } + \frac { x + 8 } { 4 }$

Perform the indicated operations involving rational numbers. Express the final answer in reduced form. $\frac { 2 } { 9 } \cdot \frac { 6 } { 13 } \div \frac { 1 } { 9 }$

It takes Amy twice as long to deliver papers as it does Nancy. How long, in minutes, would it take each girl to deliver the papers by herself if they can deliver the papers together in 60 minutes? minutes for Amy minutes for Nancy

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { n - 2 } { 6 } - \frac { n - 7 } { 9 }$

Simplify the rational expression. $\frac { - 15 x ^ { 3 } y } { - 27 x y ^ { 4 } }$