Question 1

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

Accepted Answer

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

Question 2

Perform the indicated operation and express your answer in simplest form. $\frac { 8 } { x } - \frac { 7 x + 39 } { x ^ { 2 } + 5 x } + \frac { x } { x + 5 }$

Accepted Answer

A)  $\frac { x ^ { 2 } + x + 1 } { x ( x + 5 ) }$ 
B)  $\frac { x + 1 } { x ( x + 5 ) }$ 
C)  $\frac { ( x + 1 ) ( x - 1 ) } { x ( x + 5 ) }$ 
D)  $\frac { x ^ { 2 } - x + 1 } { x ( x + 5 ) }$ 
E)  $\frac { x ^ { 2 } + x - 1 } { x ( x + 5 ) }$ 
A)  $\frac { x ^ { 2 } + x + 1 } { x ( x + 5 ) }$ 
B)  $\frac { x + 1 } { x ( x + 5 ) }$ 
C)  $\frac { ( x + 1 ) ( x - 1 ) } { x ( x + 5 ) }$ 
D)  $\frac { x ^ { 2 } - x + 1 } { x ( x + 5 ) }$ 
E)  $\frac { x ^ { 2 } + x - 1 } { x ( x + 5 ) }$

Question 3

Solve the equation. $\frac { 1 } { 9 x - 64 } = \frac { 10 } { 8 x + 16 }$

Accepted Answer

A)  x = 11 
B)  x = 9 
C)  x = 12 
D)  x = 6 
E)  x = 8 
A)  x = 11 
B)  x = 9 
C)  x = 12 
D)  x = 6 
E)  x = 8

Question 4

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 5 } { 8 x ^ { 2 } y } - \frac { 2 x } { 4 y ^ { 2 } }$

Accepted Answer

A)  $\frac { 5 y - 4 x } { 8 x ^ { 2 } y ^ { 2 } }$ 
B)  $\frac { 5 y - 4 x ^ { 3 } } { 8 x ^ { 2 } y }$ 
C)  $\frac { 5 - 4 x ^ { 3 } } { 8 x ^ { 2 } y ^ { 2 } }$ 
D)  $\frac { 5 y - 4 x ^ { 3 } } { 8 x ^ { 2 } y ^ { 2 } }$ 
A)  $\frac { 5 y - 4 x } { 8 x ^ { 2 } y ^ { 2 } }$ 
B)  $\frac { 5 y - 4 x ^ { 3 } } { 8 x ^ { 2 } y }$ 
C)  $\frac { 5 - 4 x ^ { 3 } } { 8 x ^ { 2 } y ^ { 2 } }$ 
D)  $\frac { 5 y - 4 x ^ { 3 } } { 8 x ^ { 2 } y ^ { 2 } }$

Question 5

Solve the equation. $\frac { 8 x - 47 } { 7 } = \frac { 9 } { x }$

Accepted Answer

The answer of Solve the equation. \(\frac { 8 x...

Question 6

The first step in simplifying a rational expression is to factor the numerator and the denominator, if possible.

Accepted Answer

A) True 
 B)False

Question 7

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 11 } { 45 } + \frac { 1 } { 10 }$

Accepted Answer

The answer of Perform the operation involving rational numbers. Be...

Question 8

Solve the equation. $\frac { a } { a + 11 } - 1 = \frac { 2 a } { a + 11 }$

Accepted Answer

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

Question 9

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 4 x ^ { 7 } y ^ { 7 } } { 5 x ^ { 8 } y ^ { 6 } } \cdot \frac { 35 x ^ { 7 } } { 16 y } \div \frac { y ^ { 6 } } { 4 x }$

Accepted Answer

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

Question 10

Simplify the rational expression. $\frac { 2 x ^ { 2 } + 6 x } { x ^ { 3 } + 27 }$

Accepted Answer

The answer of Simplify the rational expression. \(\frac { 2...

Question 11

If two inlet pipes are both open, they can fill a pool in 3hours and 36 minutes. One of the pipes can fill the pool by itself in 6 hours. How long, in hours, would it take the other pipe to fill the pool by itself?

Accepted Answer

A)  9 hours 
B)  6 hours 
C)  15 hours 
A)  9 hours 
B)  6 hours 
C)  15 hours

Question 12

Perform the indicated operations and express your answer in simplest form. $x - \frac { x ^ { 2 } } { x - 3 } + \frac { 3 } { x ^ { 2 } - 9 }$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 3 x + 3 } { x ^ { 2 } - 9 }$ 
B)  $\frac { - 3 x ^ { 2 } - 9 x + 3 } { ( x + 3 ) ( x - 3 ) }$ 
C)  $\frac { - 3 x ^ { 4 } - 9 x ^ { 2 } + 3 } { x ^ { 3 } + 3 x ^ { 3 } - 3 x - 27 }$ 
D)  $\frac { 3 x ^ { 2 } + 9 x + 3 } { ( x + 3 ) ( x - 3 ) }$ 
E)  $\frac { - 3 x ^ { 4 } - 9 x ^ { 2 } + 3 } { ( x + 3 ) \left( x ^ { 2 } - 9 \right) }$ 
A)  $\frac { 3 x ^ { 2 } + 3 x + 3 } { x ^ { 2 } - 9 }$ 
B)  $\frac { - 3 x ^ { 2 } - 9 x + 3 } { ( x + 3 ) ( x - 3 ) }$ 
C)  $\frac { - 3 x ^ { 4 } - 9 x ^ { 2 } + 3 } { x ^ { 3 } + 3 x ^ { 3 } - 3 x - 27 }$ 
D)  $\frac { 3 x ^ { 2 } + 9 x + 3 } { ( x + 3 ) ( x - 3 ) }$ 
E)  $\frac { - 3 x ^ { 4 } - 9 x ^ { 2 } + 3 } { ( x + 3 ) \left( x ^ { 2 } - 9 \right) }$

Question 13

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

Accepted Answer

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

Question 14

Perform the indicated operations involving rational numbers. Match each expression with the corresponding answer.
-$\frac { 3 } { 2 }$

Accepted Answer

A)  $\frac { 3 } { 8 } \cdot \frac { 4 } { 9 }$ 
B)  $\frac { 3 } { 4 } \cdot \frac { 12 } { 6 }$ 
A)  $\frac { 3 } { 8 } \cdot \frac { 4 } { 9 }$ 
B)  $\frac { 3 } { 4 } \cdot \frac { 12 } { 6 }$

Question 15

The rational express $\frac { x + 1 } { x - 4 }$ is meaninful for all values of x except $- 4$ .

Accepted Answer

A) True 
 B)False

Question 16

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 8 } { 5 n } - \frac { 6 } { 2 n ^ { 2 } }$

Accepted Answer

A)  $\frac { 8 n + 15 } { 6 n ^ { 2 } }$ 
B)  $\frac { 8 n - 15 } { 5 n ^ { 2 } }$ 
C)  $\frac { 8 n - 15 } { 5 n }$ 
D)  $\frac { 8 n - 30 } { 10 n ^ { 2 } }$ 
A)  $\frac { 8 n + 15 } { 6 n ^ { 2 } }$ 
B)  $\frac { 8 n - 15 } { 5 n ^ { 2 } }$ 
C)  $\frac { 8 n - 15 } { 5 n }$ 
D)  $\frac { 8 n - 30 } { 10 n ^ { 2 } }$

Question 17

Perform the indicated operation. $\frac { n } { n - 7 } + \frac { n + 5 } { n + 5 } + \frac { 8 n + 35 } { n ^ { 2 } - 2 n - 35 }$

Accepted Answer

A)  $\frac { 2 n ( n + 11 ) } { ( n + 7 ) ( n - 5 ) }$ 
B)  $\frac { n ( 2 n + 11 ) } { ( n - 7 ) ( n + 5 ) }$ 
C)  $\frac { n ( 2 n + 11 ) } { ( n + 7 ) ( n - 5 ) }$ 
A)  $\frac { 2 n ( n + 11 ) } { ( n + 7 ) ( n - 5 ) }$ 
B)  $\frac { n ( 2 n + 11 ) } { ( n - 7 ) ( n + 5 ) }$ 
C)  $\frac { n ( 2 n + 11 ) } { ( n + 7 ) ( n - 5 ) }$

Question 18

Perform the indicated operation and express your answer in simplest form. $$\frac { 5 } { x ^ { 2 } + 1 } - \frac { 2 } { x ^ { 2 } + 5 x - 6 }$$ 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

Perform the indicated operation involving rational numbers. $\left( - \frac { 5 } { 6 } \right) \div \frac { 20 } { 42 }$

Accepted Answer

A)  $-$ 4 
B)  $- \frac { 7 } { 4 }$ 
C)  $- \frac { 4 } { 7 }$ 
D)  $-$ 7 
A)  $-$ 4 
B)  $- \frac { 7 } { 4 }$ 
C)  $- \frac { 4 } { 7 }$ 
D)  $-$ 7

Question 20

Simplify the complex fraction. $\frac { \frac { 7 } { x } - \frac { 2 } { y } } { \frac { 7 } { y } - \frac { 2 } { x y } }$

Accepted Answer

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

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

Perform the indicated operation and express your answer in simplest form. $\frac { 8 } { x } - \frac { 7 x + 39 } { x ^ { 2 } + 5 x } + \frac { x } { x + 5 }$

Solve the equation. $\frac { 1 } { 9 x - 64 } = \frac { 10 } { 8 x + 16 }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 5 } { 8 x ^ { 2 } y } - \frac { 2 x } { 4 y ^ { 2 } }$

Solve the equation. $\frac { 8 x - 47 } { 7 } = \frac { 9 } { x }$

The first step in simplifying a rational expression is to factor the numerator and the denominator, if possible.

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 11 } { 45 } + \frac { 1 } { 10 }$

Solve the equation. $\frac { a } { a + 11 } - 1 = \frac { 2 a } { a + 11 }$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 4 x ^ { 7 } y ^ { 7 } } { 5 x ^ { 8 } y ^ { 6 } } \cdot \frac { 35 x ^ { 7 } } { 16 y } \div \frac { y ^ { 6 } } { 4 x }$

Simplify the rational expression. $\frac { 2 x ^ { 2 } + 6 x } { x ^ { 3 } + 27 }$

If two inlet pipes are both open, they can fill a pool in 3hours and 36 minutes. One of the pipes can fill the pool by itself in 6 hours. How long, in hours, would it take the other pipe to fill the pool by itself?

Perform the indicated operations and express your answer in simplest form. $x - \frac { x ^ { 2 } } { x - 3 } + \frac { 3 } { x ^ { 2 } - 9 }$

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

Perform the indicated operations involving rational numbers. Match each expression with the corresponding answer. - $\frac { 3 } { 2 }$

The rational express $\frac { x + 1 } { x - 4 }$ is meaninful for all values of x except $- 4$ .

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 8 } { 5 n } - \frac { 6 } { 2 n ^ { 2 } }$

Perform the indicated operation. $\frac { n } { n - 7 } + \frac { n + 5 } { n + 5 } + \frac { 8 n + 35 } { n ^ { 2 } - 2 n - 35 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 5 } { x ^ { 2 } + 1 } - \frac { 2 } { x ^ { 2 } + 5 x - 6 }$ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation involving rational numbers. $\left( - \frac { 5 } { 6 } \right) \div \frac { 20 } { 42 }$

Simplify the complex fraction. $\frac { \frac { 7 } { x } - \frac { 2 } { y } } { \frac { 7 } { y } - \frac { 2 } { x y } }$

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. x2+2x−2420−x−x2\frac { x ^ { 2 } + 2 x - 24 } { 20 - x - x ^ { 2 } }20−x−x2x2+2x−24​

Perform the indicated operation and express your answer in simplest form. 8x−7x+39x2+5x+xx+5\frac { 8 } { x } - \frac { 7 x + 39 } { x ^ { 2 } + 5 x } + \frac { x } { x + 5 }x8​−x2+5x7x+39​+x+5x​

Solve the equation. 19x−64=108x+16\frac { 1 } { 9 x - 64 } = \frac { 10 } { 8 x + 16 }9x−641​=8x+1610​

Subtract the rational expressions. Be sure to express your answer in simplest form. 58x2y−2x4y2\frac { 5 } { 8 x ^ { 2 } y } - \frac { 2 x } { 4 y ^ { 2 } }8x2y5​−4y22x​

Solve the equation. 8x−477=9x\frac { 8 x - 47 } { 7 } = \frac { 9 } { x }78x−47​=x9​

The first step in simplifying a rational expression is to factor the numerator and the denominator, if possible.

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. 1145+110\frac { 11 } { 45 } + \frac { 1 } { 10 }4511​+101​

Solve the equation. aa+11−1=2aa+11\frac { a } { a + 11 } - 1 = \frac { 2 a } { a + 11 }a+11a​−1=a+112a​

Perform the indicated operation involving rational expressions. Express final answer in simplest form. 4x7y75x8y6⋅35x716y÷y64x\frac { 4 x ^ { 7 } y ^ { 7 } } { 5 x ^ { 8 } y ^ { 6 } } \cdot \frac { 35 x ^ { 7 } } { 16 y } \div \frac { y ^ { 6 } } { 4 x }5x8y64x7y7​⋅16y35x7​÷4xy6​

Simplify the rational expression. 2x2+6xx3+27\frac { 2 x ^ { 2 } + 6 x } { x ^ { 3 } + 27 }x3+272x2+6x​

If two inlet pipes are both open, they can fill a pool in 3hours and 36 minutes. One of the pipes can fill the pool by itself in 6 hours. How long, in hours, would it take the other pipe to fill the pool by itself?

Perform the indicated operations and express your answer in simplest form. x−x2x−3+3x2−9x - \frac { x ^ { 2 } } { x - 3 } + \frac { 3 } { x ^ { 2 } - 9 }x−x−3x2​+x2−93​

Perform the indicated operation involving rational expressions. Express final answer in reduced form. 2x+69y÷x2+6x+9x2+2\frac { 2 x + 6 } { 9 y } \div \frac { x ^ { 2 } + 6 x + 9 } { x ^ { 2 } + 2 }9y2x+6​÷x2+2x2+6x+9​

Perform the indicated operations involving rational numbers. Match each expression with the corresponding answer. - 32\frac { 3 } { 2 }23​

The rational express x+1x−4\frac { x + 1 } { x - 4 }x−4x+1​ is meaninful for all values of x except −4- 4−4 .

Subtract the rational expressions. Be sure to express your answer in simplest form. 85n−62n2\frac { 8 } { 5 n } - \frac { 6 } { 2 n ^ { 2 } }5n8​−2n26​

Perform the indicated operation. nn−7+n+5n+5+8n+35n2−2n−35\frac { n } { n - 7 } + \frac { n + 5 } { n + 5 } + \frac { 8 n + 35 } { n ^ { 2 } - 2 n - 35 }n−7n​+n+5n+5​+n2−2n−358n+35​

Perform the indicated operation and express your answer in simplest form. 5x2+1−2x2+5x−6\frac { 5 } { x ^ { 2 } + 1 } - \frac { 2 } { x ^ { 2 } + 5 x - 6 }x2+15​−x2+5x−62​ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation involving rational numbers. (−56)÷2042\left( - \frac { 5 } { 6 } \right) \div \frac { 20 } { 42 }(−65​)÷4220​

Simplify the complex fraction. 7x−2y7y−2xy\frac { \frac { 7 } { x } - \frac { 2 } { y } } { \frac { 7 } { y } - \frac { 2 } { x y } }y7​−xy2​x7​−y2​​

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. $\frac { x ^ { 2 } + 2 x - 24 } { 20 - x - x ^ { 2 } }$

Perform the indicated operation and express your answer in simplest form. $\frac { 8 } { x } - \frac { 7 x + 39 } { x ^ { 2 } + 5 x } + \frac { x } { x + 5 }$

Solve the equation. $\frac { 1 } { 9 x - 64 } = \frac { 10 } { 8 x + 16 }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 5 } { 8 x ^ { 2 } y } - \frac { 2 x } { 4 y ^ { 2 } }$

Solve the equation. $\frac { 8 x - 47 } { 7 } = \frac { 9 } { x }$

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 11 } { 45 } + \frac { 1 } { 10 }$

Solve the equation. $\frac { a } { a + 11 } - 1 = \frac { 2 a } { a + 11 }$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 4 x ^ { 7 } y ^ { 7 } } { 5 x ^ { 8 } y ^ { 6 } } \cdot \frac { 35 x ^ { 7 } } { 16 y } \div \frac { y ^ { 6 } } { 4 x }$

Simplify the rational expression. $\frac { 2 x ^ { 2 } + 6 x } { x ^ { 3 } + 27 }$

Perform the indicated operations and express your answer in simplest form. $x - \frac { x ^ { 2 } } { x - 3 } + \frac { 3 } { x ^ { 2 } - 9 }$

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

Perform the indicated operations involving rational numbers. Match each expression with the corresponding answer. - $\frac { 3 } { 2 }$

The rational express $\frac { x + 1 } { x - 4 }$ is meaninful for all values of x except $- 4$ .

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 8 } { 5 n } - \frac { 6 } { 2 n ^ { 2 } }$

Perform the indicated operation. $\frac { n } { n - 7 } + \frac { n + 5 } { n + 5 } + \frac { 8 n + 35 } { n ^ { 2 } - 2 n - 35 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 5 } { x ^ { 2 } + 1 } - \frac { 2 } { x ^ { 2 } + 5 x - 6 }$ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation involving rational numbers. $\left( - \frac { 5 } { 6 } \right) \div \frac { 20 } { 42 }$

Simplify the complex fraction. $\frac { \frac { 7 } { x } - \frac { 2 } { y } } { \frac { 7 } { y } - \frac { 2 } { x y } }$