Question 1

Solve each equation for D . Match each equation with the corresponding solution.
-$D = \frac { Q X } { X - Q }$

Accepted Answer

A)  $\frac { D } { Q } = \frac { X } { Q + X }$ 
B)  $\frac { 1 } { D } = \frac { 1 } { Q } - \frac { 1 } { X }$ 
A)  $\frac { D } { Q } = \frac { X } { Q + X }$ 
B)  $\frac { 1 } { D } = \frac { 1 } { Q } - \frac { 1 } { X }$

Question 2

Simplify the rational expression. $\frac { 4 x ^ { 2 } y + 8 x y ^ { 2 } - 12 y ^ { 3 } } { 30 x ^ { 3 } y - 20 x ^ { 2 } y ^ { 2 } - 10 x y ^ { 3 } }$

Accepted Answer

A)  $\frac { 2 } { 5 x }$ 
B)  $\frac { 2 ( x - 3 y ) } { 5 x y ( 3 x - y ) }$ 
C)  $\frac { 2 ( x + 3 y ) } { 5 x ( 3 x + y ) }$ 
D)  $\frac { 2 y ( x + 3 y ) } { 5 x ( x - 3 y ) }$ 
A)  $\frac { 2 } { 5 x }$ 
B)  $\frac { 2 ( x - 3 y ) } { 5 x y ( 3 x - y ) }$ 
C)  $\frac { 2 ( x + 3 y ) } { 5 x ( 3 x + y ) }$ 
D)  $\frac { 2 y ( x + 3 y ) } { 5 x ( x - 3 y ) }$

Question 3

Perform the indicated operations involving rational expressions. Express the final answer in simplest form. $\frac { 12 x ^ { 2 } - 5 x - 3 } { 8 x ^ { 2 } - 2 x - 3 } \div \frac { 21 x ^ { 2 } + x - 2 } { 2 x ^ { 2 } - 17 x - 9 }$

Accepted Answer

A)  $\frac { x - 8 } { 7 x - 3 }$ 
B)  $\frac { x - 9 } { 7 x - 2 }$ 
C)  $\frac { x + 9 } { 7 x + 2 }$ 
D)  $\frac { x + 9 } { 7 x + 3 }$ 
E)  $\frac { x - 8 } { 7 x - 2 }$ 
A)  $\frac { x - 8 } { 7 x - 3 }$ 
B)  $\frac { x - 9 } { 7 x - 2 }$ 
C)  $\frac { x + 9 } { 7 x + 2 }$ 
D)  $\frac { x + 9 } { 7 x + 3 }$ 
E)  $\frac { x - 8 } { 7 x - 2 }$

Question 4

Perform the indicated operation involving rational expressions. $\frac { - 6 x y ^ { 4 } } { 7 y ^ { 2 } } \cdot \frac { 77 x ^ { 2 } y ^ { 3 } } { 24 y ^ { 2 } }$

Accepted Answer

A)  $- \frac { 11 x ^ { 2 } y ^ { 2 } } { 4 }$ 
B)  $- \frac { x ^ { 3 } y ^ { 3 } } { 11 }$ 
C)  $- \frac { 11 x ^ { 3 } y ^ { 3 } } { 4 }$ 
D)  $- \frac { 4 } { 11 x ^ { 3 } y ^ { 3 } }$ 
A)  $- \frac { 11 x ^ { 2 } y ^ { 2 } } { 4 }$ 
B)  $- \frac { x ^ { 3 } y ^ { 3 } } { 11 }$ 
C)  $- \frac { 11 x ^ { 3 } y ^ { 3 } } { 4 }$ 
D)  $- \frac { 4 } { 11 x ^ { 3 } y ^ { 3 } }$

Question 5

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 5 a ^ { 5 } b ^ { 5 } } { 6 a ^ { 4 } b ^ { 4 } } \cdot \frac { 18 a ^ { 6 } } { 10 a ^ { 4 } b ^ { 5 } }$

Accepted Answer

The answer of Perform the indicated operation involving rational expressions....

Question 6

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 4 } { 7 x - 3 } - \frac { 3 } { 5 x + 4 }$

Accepted Answer

A)  $\frac { - x + 25 } { ( 7 x - 3 ) ( 5 x + 4 ) }$ 
B)  $\frac { x - 25 } { ( 7 x - 3 ) ( 5 x + 4 ) }$ 
C)  $\frac { - x + 25 } { ( 7 x + 3 ) ( 5 x - 4 ) }$ 
D)  $\frac { - x + 41 } { ( 7 x - 3 ) ( 5 x + 4 ) }$ 
A)  $\frac { - x + 25 } { ( 7 x - 3 ) ( 5 x + 4 ) }$ 
B)  $\frac { x - 25 } { ( 7 x - 3 ) ( 5 x + 4 ) }$ 
C)  $\frac { - x + 25 } { ( 7 x + 3 ) ( 5 x - 4 ) }$ 
D)  $\frac { - x + 41 } { ( 7 x - 3 ) ( 5 x + 4 ) }$

Question 7

Simplify the rational expression. You will need to use factoring by grouping. $\frac { n r - 10 - 2 n + 5 r } { n r + 20 + 5 r + 4 n }$

Accepted Answer

The answer of Simplify the rational expression. You will need...

Question 8

Consider the addition problem. $\frac { 8 } { x - 2 } + \frac { 5 } { 2 - x }$ Note that the denominators are opposites of each other. If the property $\frac { a } { - b } = - \frac { a } { b }$ is applied to the second fraction, we have $\frac { 5 } { 2 - x } = - \frac { 5 } { x - 2 }$ Thus we proceed as follows: $\frac { 8 } { x - 2 } + \frac { 5 } { 2 - x } = \frac { 8 } { x - 2 } - \frac { 5 } { x - 2 } = \frac { 8 - 5 } { x - 2 } = \frac { 3 } { x - 2 }$ Use this approach to do the following problem. $\frac { 9 } { a - 7 } - \frac { 5 } { 7 - a }$

Accepted Answer

A)  $- \frac { 15 } { 7 - a }$ 
B)  $\frac { 14 } { a - 7 }$ 
C)  $\frac { 9 } { 7 - a }$ 
D)  $\frac { 14 } { 7 - a }$ 
A)  $- \frac { 15 } { 7 - a }$ 
B)  $\frac { 14 } { a - 7 }$ 
C)  $\frac { 9 } { 7 - a }$ 
D)  $\frac { 14 } { 7 - a }$

Question 9

Solve each equation for D . Match each equation with the corresponding solution.
-$D = \frac { Q X } { Q + X }$

Accepted Answer

A)  $\frac { D } { Q } = \frac { X } { Q + X }$ 
B)  $\frac { 1 } { D } = \frac { 1 } { Q } - \frac { 1 } { X }$ 
A)  $\frac { D } { Q } = \frac { X } { Q + X }$ 
B)  $\frac { 1 } { D } = \frac { 1 } { Q } - \frac { 1 } { X }$

Question 10

Simplify the complex fraction. $\frac { \frac { 3 } { 6 x } } { \frac { 9 } { 2 x y } }$

Accepted Answer

The answer of Simplify the complex fraction. \(\frac { \frac...

Question 11

Perform the indicated operation and express your answer in simplest form. $$\frac { 4 } { x ^ { 2 } + 9 x + 8 } + \frac { - 3 } { 2 x ^ { 2 } + 19 x + 24 }$$ 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 12

Perform the indicated operation. $\frac { 4 } { x } - \frac { 3 x + 15 } { x ^ { 2 } + 4 x } + \frac { x } { x + 4 }$

Accepted Answer

A)  $\frac { x ^ { 2 } + x - 1 } { x ( x + 4 ) }$ 
B)  $\frac { x ^ { 2 } + x + 1 } { x ( x + 4 ) }$ 
C)  $\frac { x ^ { 2 } - x + 1 } { x ( x + 4 ) }$ 
A)  $\frac { x ^ { 2 } + x - 1 } { x ( x + 4 ) }$ 
B)  $\frac { x ^ { 2 } + x + 1 } { x ( x + 4 ) }$ 
C)  $\frac { x ^ { 2 } - x + 1 } { x ( x + 4 ) }$

Question 13

Solve each equation for the variable N . $\frac { N } { S } = \frac { T } { S + T }$

Accepted Answer

A)  $N = \frac { S T } { T - S }$ 
B)  $N = \frac { S T } { S - T }$ 
C)  $N = \frac { S T } { S + T }$ 
A)  $N = \frac { S T } { T - S }$ 
B)  $N = \frac { S T } { S - T }$ 
C)  $N = \frac { S T } { S + T }$

Question 14

Solve the equation. $\frac { x + 1 } { 5 } + \frac { x - 3 } { 4 } = \frac { 4 } { 5 }$

Accepted Answer

The answer of Solve the equation. \(\frac { x +...

Question 15

Perform the indicated operations involving rational expressions. Express the final answer in simplest form. $\frac { 3 x ^ { 2 } - 20 x + 25 } { 2 x ^ { 2 } - 7 x - 15 } \div \frac { 9 x ^ { 2 } - 3 x - 20 } { 12 x ^ { 2 } + 28 x + 15 }$

Accepted Answer

A)  $\frac { 6 x - 5 } { 3 x - 2 }$ 
B)  $\frac { 6 x + 5 } { 3 x + 4 }$ 
C)  $\frac { 6 x + 9 } { 3 x + 4 }$ 
D)  $\frac { 6 x - 5 } { 3 x - 4 }$ 
E)  $\frac { 6 x + 9 } { 3 x + 2 }$ 
A)  $\frac { 6 x - 5 } { 3 x - 2 }$ 
B)  $\frac { 6 x + 5 } { 3 x + 4 }$ 
C)  $\frac { 6 x + 9 } { 3 x + 4 }$ 
D)  $\frac { 6 x - 5 } { 3 x - 4 }$ 
E)  $\frac { 6 x + 9 } { 3 x + 2 }$

Question 16

Perform the indicated operation. $\frac { x } { x ^ { 2 } - 4 } + \frac { 6 } { x - 2 }$

Accepted Answer

A)  $\frac { 7 x - 6 } { ( x + 2 ) ( x - 2 ) }$ 
B)  $\frac { 7 x - 12 } { x - 2 }$ 
C)  $\frac { 7 x - 12 } { x + 2 }$ 
D)  $\frac { 7 x + 12 } { ( x + 2 ) ( x - 2 ) }$ 
A)  $\frac { 7 x - 6 } { ( x + 2 ) ( x - 2 ) }$ 
B)  $\frac { 7 x - 12 } { x - 2 }$ 
C)  $\frac { 7 x - 12 } { x + 2 }$ 
D)  $\frac { 7 x + 12 } { ( x + 2 ) ( x - 2 ) }$

Question 17

The rational expression $\frac { \frac { 2 } { 9 } - \frac { 4 } { 7 } } { 5 }$ is a complex fraction.

Accepted Answer

A) True 
 B)False

Question 18

Simplify the complex fraction. $\frac { \frac { 1 } { 5 } - \frac { 1 } { 10 } } { \frac { 11 } { 15 } + \frac { 9 } { 10 } }$

Accepted Answer

A)  $\frac { 3 } { 49 }$ 
B)  $\frac { 1 } { 49 }$ 
C)  $\frac { 3 } { 51 }$ 
D)  $\frac { 1 } { 51 }$ 
A)  $\frac { 3 } { 49 }$ 
B)  $\frac { 1 } { 49 }$ 
C)  $\frac { 3 } { 51 }$ 
D)  $\frac { 1 } { 51 }$

Question 19

Express the rational number in reduced form. $\frac { 24 } { 30 }$

Accepted Answer

A)  $\frac { 4 } { 5 }$ 
B)  $\frac { 5 } { 6 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $\frac { 4 } { 5 }$ 
B)  $\frac { 5 } { 6 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 2 }$

Question 20

If a person can do a job in h hours, then at the end of 3 hours he or she will have completed $\frac { 3 } { n }$ of the job.

Accepted Answer

A) True 
 B)False

Solve each equation for D . Match each equation with the corresponding solution. - $D = \frac { Q X } { X - Q }$

Simplify the rational expression. $\frac { 4 x ^ { 2 } y + 8 x y ^ { 2 } - 12 y ^ { 3 } } { 30 x ^ { 3 } y - 20 x ^ { 2 } y ^ { 2 } - 10 x y ^ { 3 } }$

Perform the indicated operations involving rational expressions. Express the final answer in simplest form. $\frac { 12 x ^ { 2 } - 5 x - 3 } { 8 x ^ { 2 } - 2 x - 3 } \div \frac { 21 x ^ { 2 } + x - 2 } { 2 x ^ { 2 } - 17 x - 9 }$

Perform the indicated operation involving rational expressions. $\frac { - 6 x y ^ { 4 } } { 7 y ^ { 2 } } \cdot \frac { 77 x ^ { 2 } y ^ { 3 } } { 24 y ^ { 2 } }$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 5 a ^ { 5 } b ^ { 5 } } { 6 a ^ { 4 } b ^ { 4 } } \cdot \frac { 18 a ^ { 6 } } { 10 a ^ { 4 } b ^ { 5 } }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 4 } { 7 x - 3 } - \frac { 3 } { 5 x + 4 }$

Simplify the rational expression. You will need to use factoring by grouping. $\frac { n r - 10 - 2 n + 5 r } { n r + 20 + 5 r + 4 n }$

Solve each equation for D . Match each equation with the corresponding solution. - $D = \frac { Q X } { Q + X }$

Simplify the complex fraction. $\frac { \frac { 3 } { 6 x } } { \frac { 9 } { 2 x y } }$

Perform the indicated operation and express your answer in simplest form. $\frac { 4 } { x ^ { 2 } + 9 x + 8 } + \frac { - 3 } { 2 x ^ { 2 } + 19 x + 24 }$ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation. $\frac { 4 } { x } - \frac { 3 x + 15 } { x ^ { 2 } + 4 x } + \frac { x } { x + 4 }$

Solve each equation for the variable N . $\frac { N } { S } = \frac { T } { S + T }$

Solve the equation. $\frac { x + 1 } { 5 } + \frac { x - 3 } { 4 } = \frac { 4 } { 5 }$

Perform the indicated operations involving rational expressions. Express the final answer in simplest form. $\frac { 3 x ^ { 2 } - 20 x + 25 } { 2 x ^ { 2 } - 7 x - 15 } \div \frac { 9 x ^ { 2 } - 3 x - 20 } { 12 x ^ { 2 } + 28 x + 15 }$

Perform the indicated operation. $\frac { x } { x ^ { 2 } - 4 } + \frac { 6 } { x - 2 }$

The rational expression $\frac { \frac { 2 } { 9 } - \frac { 4 } { 7 } } { 5 }$ is a complex fraction.

Simplify the complex fraction. $\frac { \frac { 1 } { 5 } - \frac { 1 } { 10 } } { \frac { 11 } { 15 } + \frac { 9 } { 10 } }$

Express the rational number in reduced form. $\frac { 24 } { 30 }$

If a person can do a job in h hours, then at the end of 3 hours he or she will have completed $\frac { 3 } { n }$ of the job.

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

Solve each equation for D . Match each equation with the corresponding solution. - D=QXX−QD = \frac { Q X } { X - Q }D=X−QQX​

Simplify the rational expression. 4x2y+8xy2−12y330x3y−20x2y2−10xy3\frac { 4 x ^ { 2 } y + 8 x y ^ { 2 } - 12 y ^ { 3 } } { 30 x ^ { 3 } y - 20 x ^ { 2 } y ^ { 2 } - 10 x y ^ { 3 } }30x3y−20x2y2−10xy34x2y+8xy2−12y3​

Perform the indicated operation involving rational expressions. −6xy47y2⋅77x2y324y2\frac { - 6 x y ^ { 4 } } { 7 y ^ { 2 } } \cdot \frac { 77 x ^ { 2 } y ^ { 3 } } { 24 y ^ { 2 } }7y2−6xy4​⋅24y277x2y3​

Perform the indicated operation involving rational expressions. Express final answer in simplest form. 5a5b56a4b4⋅18a610a4b5\frac { 5 a ^ { 5 } b ^ { 5 } } { 6 a ^ { 4 } b ^ { 4 } } \cdot \frac { 18 a ^ { 6 } } { 10 a ^ { 4 } b ^ { 5 } }6a4b45a5b5​⋅10a4b518a6​

Subtract the rational expressions. Be sure to express your answer in simplest form. 47x−3−35x+4\frac { 4 } { 7 x - 3 } - \frac { 3 } { 5 x + 4 }7x−34​−5x+43​

Simplify the rational expression. You will need to use factoring by grouping. nr−10−2n+5rnr+20+5r+4n\frac { n r - 10 - 2 n + 5 r } { n r + 20 + 5 r + 4 n }nr+20+5r+4nnr−10−2n+5r​

Solve each equation for D . Match each equation with the corresponding solution. - D=QXQ+XD = \frac { Q X } { Q + X }D=Q+XQX​

Simplify the complex fraction. 36x92xy\frac { \frac { 3 } { 6 x } } { \frac { 9 } { 2 x y } }2xy9​6x3​​

Perform the indicated operation and express your answer in simplest form. 4x2+9x+8+−32x2+19x+24\frac { 4 } { x ^ { 2 } + 9 x + 8 } + \frac { - 3 } { 2 x ^ { 2 } + 19 x + 24 }x2+9x+84​+2x2+19x+24−3​ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation. 4x−3x+15x2+4x+xx+4\frac { 4 } { x } - \frac { 3 x + 15 } { x ^ { 2 } + 4 x } + \frac { x } { x + 4 }x4​−x2+4x3x+15​+x+4x​

Solve each equation for the variable N . NS=TS+T\frac { N } { S } = \frac { T } { S + T }SN​=S+TT​

Solve the equation. x+15+x−34=45\frac { x + 1 } { 5 } + \frac { x - 3 } { 4 } = \frac { 4 } { 5 }5x+1​+4x−3​=54​

Perform the indicated operation. xx2−4+6x−2\frac { x } { x ^ { 2 } - 4 } + \frac { 6 } { x - 2 }x2−4x​+x−26​

The rational expression 29−475\frac { \frac { 2 } { 9 } - \frac { 4 } { 7 } } { 5 }592​−74​​ is a complex fraction.

Simplify the complex fraction. 15−1101115+910\frac { \frac { 1 } { 5 } - \frac { 1 } { 10 } } { \frac { 11 } { 15 } + \frac { 9 } { 10 } }1511​+109​51​−101​​

Express the rational number in reduced form. 2430\frac { 24 } { 30 }3024​

If a person can do a job in h hours, then at the end of 3 hours he or she will have completed 3n\frac { 3 } { n }n3​ of the job.

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

Solve each equation for D . Match each equation with the corresponding solution. - $D = \frac { Q X } { X - Q }$

Simplify the rational expression. $\frac { 4 x ^ { 2 } y + 8 x y ^ { 2 } - 12 y ^ { 3 } } { 30 x ^ { 3 } y - 20 x ^ { 2 } y ^ { 2 } - 10 x y ^ { 3 } }$

Perform the indicated operation involving rational expressions. $\frac { - 6 x y ^ { 4 } } { 7 y ^ { 2 } } \cdot \frac { 77 x ^ { 2 } y ^ { 3 } } { 24 y ^ { 2 } }$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 5 a ^ { 5 } b ^ { 5 } } { 6 a ^ { 4 } b ^ { 4 } } \cdot \frac { 18 a ^ { 6 } } { 10 a ^ { 4 } b ^ { 5 } }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 4 } { 7 x - 3 } - \frac { 3 } { 5 x + 4 }$

Simplify the rational expression. You will need to use factoring by grouping. $\frac { n r - 10 - 2 n + 5 r } { n r + 20 + 5 r + 4 n }$

Solve each equation for D . Match each equation with the corresponding solution. - $D = \frac { Q X } { Q + X }$

Simplify the complex fraction. $\frac { \frac { 3 } { 6 x } } { \frac { 9 } { 2 x y } }$

Perform the indicated operation and express your answer in simplest form. $\frac { 4 } { x ^ { 2 } + 9 x + 8 } + \frac { - 3 } { 2 x ^ { 2 } + 19 x + 24 }$ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation. $\frac { 4 } { x } - \frac { 3 x + 15 } { x ^ { 2 } + 4 x } + \frac { x } { x + 4 }$

Solve each equation for the variable N . $\frac { N } { S } = \frac { T } { S + T }$

Solve the equation. $\frac { x + 1 } { 5 } + \frac { x - 3 } { 4 } = \frac { 4 } { 5 }$

Perform the indicated operation. $\frac { x } { x ^ { 2 } - 4 } + \frac { 6 } { x - 2 }$

The rational expression $\frac { \frac { 2 } { 9 } - \frac { 4 } { 7 } } { 5 }$ is a complex fraction.

Simplify the complex fraction. $\frac { \frac { 1 } { 5 } - \frac { 1 } { 10 } } { \frac { 11 } { 15 } + \frac { 9 } { 10 } }$

Express the rational number in reduced form. $\frac { 24 } { 30 }$

If a person can do a job in h hours, then at the end of 3 hours he or she will have completed $\frac { 3 } { n }$ of the job.