Question 1

Solve the equation. $\frac { x } { x - 3 } - \frac { 4 } { x + 7 } = \frac { 52 } { x ^ { 2 } + 4 x - 21 }$

Accepted Answer

A)  x = -5, x = 8 
B)  x = 5, x = 8 
C)  x = 5, x = $-$ 8 
A)  x = -5, x = 8 
B)  x = 5, x = 8 
C)  x = 5, x = $-$ 8

Question 2

Simplify the rational expression. $\frac { x ^ { 4 } - 2 x ^ { 2 } - 24 } { 2 x ^ { 4 } + 13 x ^ { 2 } + 20 }$

Accepted Answer

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

Question 3

Simplify the rational expression. You will need to use factoring by grouping. $\frac { x y + c y + k x + c k } { x y + c y + s x + c s }$

Accepted Answer

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

Question 4

Perform the indicated operation involving rational expressions. $\frac { 3 a ^ { 5 } b ^ { 5 } } { 4 a ^ { 4 } c b ^ { 4 } } \div \frac { 6 c a ^ { 4 } b ^ { 5 } } { 20 a ^ { 6 } }$

Accepted Answer

A)  $\frac { 5 a ^ { 2 } c ^ { 2 } } { 2 b ^ { 5 } }$ 
B)  $\frac { 2 a ^ { 3 } } { 5 b ^ { 4 } }$ 
C)  $\frac { 5 a ^ { 3 } } { 2 b ^ { 4 } c ^ { 2 } }$ 
D)  $\frac { 5 a ^ { 3 } } { b ^ { 5 } c }$ 
A)  $\frac { 5 a ^ { 2 } c ^ { 2 } } { 2 b ^ { 5 } }$ 
B)  $\frac { 2 a ^ { 3 } } { 5 b ^ { 4 } }$ 
C)  $\frac { 5 a ^ { 3 } } { 2 b ^ { 4 } c ^ { 2 } }$ 
D)  $\frac { 5 a ^ { 3 } } { b ^ { 5 } c }$

Question 5

Perform the indicated operation. $\frac { 4 x + 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 x + 1 } { x ^ { 2 } + 6 x + 8 } + \frac { 6 } { x + 4 }$

Accepted Answer

A)  $\frac { 14 x ^ { 2 } + 76 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$ 
B)  $\frac { 13 x ^ { 2 } + 76 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$ 
C)  $\frac { 13 x ^ { 2 } + 79 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$ 
D)  $\frac { 13 x ^ { 2 } + 76 x + 69 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$ 
A)  $\frac { 14 x ^ { 2 } + 76 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$ 
B)  $\frac { 13 x ^ { 2 } + 76 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$ 
C)  $\frac { 13 x ^ { 2 } + 79 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$ 
D)  $\frac { 13 x ^ { 2 } + 76 x + 69 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$

Question 6

Solve the equation. $\frac { x } { x - 4 } - \frac { 8 } { x + 12 } = \frac { 149 } { x ^ { 2 } + 8 x - 48 }$

Accepted Answer

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

Question 7

Perform the indicated operation involving rational expressions. Express final answer in reduced form. $\frac { 6 a ^ { 2 } - 12 a } { a ^ { 3 } - 7 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 14 a + 49 } { a ^ { 2 } - 4 }$

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Simplify the rational expression. $\frac { a ^ { 2 } + 5 a + 6 } { a ^ { 2 } - 6 a - 27 }$

Accepted Answer

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

Question 10

Perform the indicated operation and express your answer in simplest form. $$\frac { 22 x + 68 } { x ^ { 2 } - 25 } - \frac { 9 } { x - 5 }$$ 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 11

One method for simplifying a complex fraction is to multiply the entire fraction by 1.

Accepted Answer

A) True 
 B)False

Question 12

Perform the indicated operation and express your answer in simplest form. $\frac { 3 x } { x ^ { 2 } - 10 x + 25 } - \frac { 2 } { x - 5 }$

Accepted Answer

A)  $\frac { x + 10 } { x - 5 }$ 
B)  $\frac { 3 x - 2 } { x - 5 }$ 
C)  $\frac { 10 } { x - 5 }$ 
D)  $\frac { x - 10 } { ( x - 5 ) ^ { 2 } }$ 
E)  $\frac { x + 10 } { ( x - 5 ) ^ { 2 } }$ 
A)  $\frac { x + 10 } { x - 5 }$ 
B)  $\frac { 3 x - 2 } { x - 5 }$ 
C)  $\frac { 10 } { x - 5 }$ 
D)  $\frac { x - 10 } { ( x - 5 ) ^ { 2 } }$ 
E)  $\frac { x + 10 } { ( x - 5 ) ^ { 2 } }$

Question 13

Perform the indicated operations and express your answer in simplest form. $$x - \frac { x ^ { 2 } } { x - 2 } + \frac { 6 } { x ^ { 2 } - 4 }$$

Accepted Answer

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

Question 14

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { n r + 9 n - 7 r - 63 } { n r + 5 n + 4 r + 20 } \cdot \frac { n ^ { 2 } - 16 } { n ^ { 3 } - 7 n ^ { 2 } }$

Accepted Answer

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

Question 15

Simplify the rational expression. $\frac { 20 x + 16 } { 16 x - 12 }$

Accepted Answer

A)  $\frac { 5 x + 16 } { 4 x - 12 }$ 
B)  9 
C)  $- \frac { 5 x + 4 } { 4 x + 3 }$ 
D)  $\frac { 5 x + 4 } { 4 x - 3 }$ 
A)  $\frac { 5 x + 16 } { 4 x - 12 }$ 
B)  9 
C)  $- \frac { 5 x + 4 } { 4 x + 3 }$ 
D)  $\frac { 5 x + 4 } { 4 x - 3 }$

Question 16

Perform the indicated operation involving rational expressions. $\frac { 7 x ^ { 4 } y ^ { 4 } } { 8 x ^ { 5 } y ^ { 3 } } \cdot \frac { 56 x ^ { 4 } } { 28 y } \cdot \frac { 4 x } { y ^ { 3 } }$

Accepted Answer

A)  $\frac { 7 x ^ { 4 } } { y ^ { 3 } }$ 
B)  $\frac { 4 x ^ { 4 } } { y ^ { 3 } }$ 
C)  $\frac { 7 x ^ { 4 } } { y ^ { 4 } }$ 
D)  $\frac { 7 x ^ { 3 } } { 4 y ^ { 3 } }$ 
A)  $\frac { 7 x ^ { 4 } } { y ^ { 3 } }$ 
B)  $\frac { 4 x ^ { 4 } } { y ^ { 3 } }$ 
C)  $\frac { 7 x ^ { 4 } } { y ^ { 4 } }$ 
D)  $\frac { 7 x ^ { 3 } } { 4 y ^ { 3 } }$

Question 17

Perform the indicated operation and express your answer in simplest form. $$\frac { 27 } { x ^ { 2 } + 3 x - 10 } - \frac { 4 } { x ^ { 2 } + 6 x - 16 }$$ 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 18

Simplify the rational expression. $\frac { - 4 y ^ { 3 } } { 14 x y ^ { 2 } }$

Accepted Answer

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

Question 19

Solve the equation for the variable y . $\frac { y - g } { x } = s$

Accepted Answer

The answer of Solve the equation for the variable y...

Question 20

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 2 x + 6 } { 3 y } \cdot \frac { x ^ { 2 } + 8 } { x ^ { 2 } + 6 x + 9 }$

Accepted Answer

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

Solve the equation. $\frac { x } { x - 3 } - \frac { 4 } { x + 7 } = \frac { 52 } { x ^ { 2 } + 4 x - 21 }$

Simplify the rational expression. $\frac { x ^ { 4 } - 2 x ^ { 2 } - 24 } { 2 x ^ { 4 } + 13 x ^ { 2 } + 20 }$

Simplify the rational expression. You will need to use factoring by grouping. $\frac { x y + c y + k x + c k } { x y + c y + s x + c s }$

Perform the indicated operation involving rational expressions. $\frac { 3 a ^ { 5 } b ^ { 5 } } { 4 a ^ { 4 } c b ^ { 4 } } \div \frac { 6 c a ^ { 4 } b ^ { 5 } } { 20 a ^ { 6 } }$

Perform the indicated operation. $\frac { 4 x + 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 x + 1 } { x ^ { 2 } + 6 x + 8 } + \frac { 6 } { x + 4 }$

Solve the equation. $\frac { x } { x - 4 } - \frac { 8 } { x + 12 } = \frac { 149 } { x ^ { 2 } + 8 x - 48 }$

Perform the indicated operation involving rational expressions. Express final answer in reduced form. $\frac { 6 a ^ { 2 } - 12 a } { a ^ { 3 } - 7 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 14 a + 49 } { a ^ { 2 } - 4 }$

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

Simplify the rational expression. $\frac { a ^ { 2 } + 5 a + 6 } { a ^ { 2 } - 6 a - 27 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 22 x + 68 } { x ^ { 2 } - 25 } - \frac { 9 } { x - 5 }$ Please enter your answer as one fraction with the denominator factored completely.

One method for simplifying a complex fraction is to multiply the entire fraction by 1.

Perform the indicated operation and express your answer in simplest form. $\frac { 3 x } { x ^ { 2 } - 10 x + 25 } - \frac { 2 } { x - 5 }$

Perform the indicated operations and express your answer in simplest form. $x - \frac { x ^ { 2 } } { x - 2 } + \frac { 6 } { x ^ { 2 } - 4 }$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { n r + 9 n - 7 r - 63 } { n r + 5 n + 4 r + 20 } \cdot \frac { n ^ { 2 } - 16 } { n ^ { 3 } - 7 n ^ { 2 } }$

Simplify the rational expression. $\frac { 20 x + 16 } { 16 x - 12 }$

Perform the indicated operation involving rational expressions. $\frac { 7 x ^ { 4 } y ^ { 4 } } { 8 x ^ { 5 } y ^ { 3 } } \cdot \frac { 56 x ^ { 4 } } { 28 y } \cdot \frac { 4 x } { y ^ { 3 } }$

Perform the indicated operation and express your answer in simplest form. $\frac { 27 } { x ^ { 2 } + 3 x - 10 } - \frac { 4 } { x ^ { 2 } + 6 x - 16 }$ Please enter your answer as one fraction with the denominator factored completely.

Simplify the rational expression. $\frac { - 4 y ^ { 3 } } { 14 x y ^ { 2 } }$

Solve the equation for the variable y . $\frac { y - g } { x } = s$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 2 x + 6 } { 3 y } \cdot \frac { x ^ { 2 } + 8 } { x ^ { 2 } + 6 x + 9 }$

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 the equation. xx−3−4x+7=52x2+4x−21\frac { x } { x - 3 } - \frac { 4 } { x + 7 } = \frac { 52 } { x ^ { 2 } + 4 x - 21 }x−3x​−x+74​=x2+4x−2152​

Simplify the rational expression. x4−2x2−242x4+13x2+20\frac { x ^ { 4 } - 2 x ^ { 2 } - 24 } { 2 x ^ { 4 } + 13 x ^ { 2 } + 20 }2x4+13x2+20x4−2x2−24​

Simplify the rational expression. You will need to use factoring by grouping. xy+cy+kx+ckxy+cy+sx+cs\frac { x y + c y + k x + c k } { x y + c y + s x + c s }xy+cy+sx+csxy+cy+kx+ck​

Perform the indicated operation involving rational expressions. 3a5b54a4cb4÷6ca4b520a6\frac { 3 a ^ { 5 } b ^ { 5 } } { 4 a ^ { 4 } c b ^ { 4 } } \div \frac { 6 c a ^ { 4 } b ^ { 5 } } { 20 a ^ { 6 } }4a4cb43a5b5​÷20a66ca4b5​

Perform the indicated operation. 4x+2x2+7x+10+3x+1x2+6x+8+6x+4\frac { 4 x + 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 x + 1 } { x ^ { 2 } + 6 x + 8 } + \frac { 6 } { x + 4 }x2+7x+104x+2​+x2+6x+83x+1​+x+46​

Solve the equation. xx−4−8x+12=149x2+8x−48\frac { x } { x - 4 } - \frac { 8 } { x + 12 } = \frac { 149 } { x ^ { 2 } + 8 x - 48 }x−4x​−x+128​=x2+8x−48149​

Perform the indicated operation involving rational expressions. Express final answer in reduced form. 6a2−12aa3−7a2⋅a2−14a+49a2−4\frac { 6 a ^ { 2 } - 12 a } { a ^ { 3 } - 7 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 14 a + 49 } { a ^ { 2 } - 4 }a3−7a26a2−12a​⋅a2−4a2−14a+49​

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

Simplify the rational expression. a2+5a+6a2−6a−27\frac { a ^ { 2 } + 5 a + 6 } { a ^ { 2 } - 6 a - 27 }a2−6a−27a2+5a+6​

Perform the indicated operation and express your answer in simplest form. 22x+68x2−25−9x−5\frac { 22 x + 68 } { x ^ { 2 } - 25 } - \frac { 9 } { x - 5 }x2−2522x+68​−x−59​ Please enter your answer as one fraction with the denominator factored completely.

One method for simplifying a complex fraction is to multiply the entire fraction by 1.

Perform the indicated operation and express your answer in simplest form. 3xx2−10x+25−2x−5\frac { 3 x } { x ^ { 2 } - 10 x + 25 } - \frac { 2 } { x - 5 }x2−10x+253x​−x−52​

Perform the indicated operations and express your answer in simplest form. x−x2x−2+6x2−4x - \frac { x ^ { 2 } } { x - 2 } + \frac { 6 } { x ^ { 2 } - 4 }x−x−2x2​+x2−46​

Simplify the rational expression. 20x+1616x−12\frac { 20 x + 16 } { 16 x - 12 }16x−1220x+16​

Perform the indicated operation involving rational expressions. 7x4y48x5y3⋅56x428y⋅4xy3\frac { 7 x ^ { 4 } y ^ { 4 } } { 8 x ^ { 5 } y ^ { 3 } } \cdot \frac { 56 x ^ { 4 } } { 28 y } \cdot \frac { 4 x } { y ^ { 3 } }8x5y37x4y4​⋅28y56x4​⋅y34x​

Perform the indicated operation and express your answer in simplest form. 27x2+3x−10−4x2+6x−16\frac { 27 } { x ^ { 2 } + 3 x - 10 } - \frac { 4 } { x ^ { 2 } + 6 x - 16 }x2+3x−1027​−x2+6x−164​ Please enter your answer as one fraction with the denominator factored completely.

Simplify the rational expression. −4y314xy2\frac { - 4 y ^ { 3 } } { 14 x y ^ { 2 } }14xy2−4y3​

Solve the equation for the variable y . y−gx=s\frac { y - g } { x } = sxy−g​=s

Perform the indicated operation involving rational expressions. Express final answer in simplest form. 2x+63y⋅x2+8x2+6x+9\frac { 2 x + 6 } { 3 y } \cdot \frac { x ^ { 2 } + 8 } { x ^ { 2 } + 6 x + 9 }3y2x+6​⋅x2+6x+9x2+8​

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 the equation. $\frac { x } { x - 3 } - \frac { 4 } { x + 7 } = \frac { 52 } { x ^ { 2 } + 4 x - 21 }$

Simplify the rational expression. $\frac { x ^ { 4 } - 2 x ^ { 2 } - 24 } { 2 x ^ { 4 } + 13 x ^ { 2 } + 20 }$

Simplify the rational expression. You will need to use factoring by grouping. $\frac { x y + c y + k x + c k } { x y + c y + s x + c s }$

Perform the indicated operation involving rational expressions. $\frac { 3 a ^ { 5 } b ^ { 5 } } { 4 a ^ { 4 } c b ^ { 4 } } \div \frac { 6 c a ^ { 4 } b ^ { 5 } } { 20 a ^ { 6 } }$

Perform the indicated operation. $\frac { 4 x + 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 x + 1 } { x ^ { 2 } + 6 x + 8 } + \frac { 6 } { x + 4 }$

Solve the equation. $\frac { x } { x - 4 } - \frac { 8 } { x + 12 } = \frac { 149 } { x ^ { 2 } + 8 x - 48 }$

Perform the indicated operation involving rational expressions. Express final answer in reduced form. $\frac { 6 a ^ { 2 } - 12 a } { a ^ { 3 } - 7 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 14 a + 49 } { a ^ { 2 } - 4 }$

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

Simplify the rational expression. $\frac { a ^ { 2 } + 5 a + 6 } { a ^ { 2 } - 6 a - 27 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 22 x + 68 } { x ^ { 2 } - 25 } - \frac { 9 } { x - 5 }$ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation and express your answer in simplest form. $\frac { 3 x } { x ^ { 2 } - 10 x + 25 } - \frac { 2 } { x - 5 }$

Perform the indicated operations and express your answer in simplest form. $x - \frac { x ^ { 2 } } { x - 2 } + \frac { 6 } { x ^ { 2 } - 4 }$

Simplify the rational expression. $\frac { 20 x + 16 } { 16 x - 12 }$

Perform the indicated operation involving rational expressions. $\frac { 7 x ^ { 4 } y ^ { 4 } } { 8 x ^ { 5 } y ^ { 3 } } \cdot \frac { 56 x ^ { 4 } } { 28 y } \cdot \frac { 4 x } { y ^ { 3 } }$

Perform the indicated operation and express your answer in simplest form. $\frac { 27 } { x ^ { 2 } + 3 x - 10 } - \frac { 4 } { x ^ { 2 } + 6 x - 16 }$ Please enter your answer as one fraction with the denominator factored completely.

Simplify the rational expression. $\frac { - 4 y ^ { 3 } } { 14 x y ^ { 2 } }$

Solve the equation for the variable y . $\frac { y - g } { x } = s$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 2 x + 6 } { 3 y } \cdot \frac { x ^ { 2 } + 8 } { x ^ { 2 } + 6 x + 9 }$