Question 1

Solve the equation. $4 + \frac { 12 } { t - 5 } = \frac { 12 } { t ( t - 5 ) }$

Accepted Answer

The answer of Solve the equation. \(4 + \frac {...

Question 2

Perform the indicated operation involving rational expressions. Express final answer in reduced form. $\frac { 4 t ^ { 5 } - 8 t ^ { 4 } } { t ^ { 3 } - 9 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 18 t + 81 } { t ^ { 5 } - 4 t ^ { 3 } }$

Accepted Answer

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

Question 3

The perimeter of a rectangle is 266 centimeters. If the ratio of its width to its length is 6 to 13, find the dimensions of the rectangle.

Accepted Answer

A)  The width is 42 centimeters and the length is 91 centimeters. 
B)  The width is 52 centimeters and the length is 81 centimeters. 
C)  The width is 37 centimeters and the length is 96 centimeters. 
D)  The width is 47 centimeters and the length is 86 centimeters. 
E)  The width is 32 centimeters and the length is 101 centimeters. 
A)  The width is 42 centimeters and the length is 91 centimeters. 
B)  The width is 52 centimeters and the length is 81 centimeters. 
C)  The width is 37 centimeters and the length is 96 centimeters. 
D)  The width is 47 centimeters and the length is 86 centimeters. 
E)  The width is 32 centimeters and the length is 101 centimeters.

Question 4

Solve the equation. $\frac { x } { x - 6 } - 2 = \frac { 6 } { x - 6 }$

Accepted Answer

A)  $\{ 1 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ 6 \}$ 
E)  $\phi$ 
A)  $\{ 1 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ 6 \}$ 
E)  $\phi$

Question 5

Simplify the rational expression. $\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x }$

Accepted Answer

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

Question 6

To travel 38 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen to travel 48 miles riding a bicycle. Sue travels 7 miles per hour faster than Doreen. Find the times and rates of both girls.

Accepted Answer

A)  Sue travels at 19 mph for 2 hours and Doreen travels at 12 mph for 4 hours. 
B)  Sue travels at 2 mph for 19 hours and Doreen travels at 12 mph for 4 hours. 
C)  Sue travels at 12 mph for 2 hours and Doreen travels at 19 mph for 4 hours. 
A)  Sue travels at 19 mph for 2 hours and Doreen travels at 12 mph for 4 hours. 
B)  Sue travels at 2 mph for 19 hours and Doreen travels at 12 mph for 4 hours. 
C)  Sue travels at 12 mph for 2 hours and Doreen travels at 19 mph for 4 hours.

Question 7

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 20 minutes?

Accepted Answer

A)  20 minutes for Nancy and 40 minutes for Amy 
B)  40 minutes for Nancy and 20 minutes for Amy 
C)  30 minutes for Nancy and 60 minutes for Amy 
A)  20 minutes for Nancy and 40 minutes for Amy 
B)  40 minutes for Nancy and 20 minutes for Amy 
C)  30 minutes for Nancy and 60 minutes for Amy

Question 8

Uniform motion problems are a special case of a rate-time problem.

Accepted Answer

A) True 
 B)False

Question 9

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 8 x } - \frac { 6 } { x }$

Accepted Answer

A)  $\frac { 7 x - 48 } { x ( x + 8 ) }$ 
B)  $\frac { - 7 x + 48 } { x ( x + 8 ) }$ 
C)  $\frac { x - 48 } { x ( x + 8 ) }$ 
A)  $\frac { 7 x - 48 } { x ( x + 8 ) }$ 
B)  $\frac { - 7 x + 48 } { x ( x + 8 ) }$ 
C)  $\frac { x - 48 } { x ( x + 8 ) }$

Question 10

Simplify the rational expression. $\frac { x ^ { 2 } + 5 x - 14 } { 6 - x - x ^ { 2 } }$

Accepted Answer

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

Question 11

Add or subtract the rational expressions. $\frac { 5 } { 4 x } + \frac { 6 } { 5 y } - 3$

Accepted Answer

A)  $\frac { 25 y + 24 x } { 4 x + 5 y } - 3$ 
B)  $\frac { 25 y + 24 x - 60 x y } { 20 x y }$ 
C)  $\frac { 25 y + 24 x } { 20 x y }$ 
D)  $\frac { 20 y + 30 x - 12 x - 15 y } { 4 x + 5 y }$ 
A)  $\frac { 25 y + 24 x } { 4 x + 5 y } - 3$ 
B)  $\frac { 25 y + 24 x - 60 x y } { 20 x y }$ 
C)  $\frac { 25 y + 24 x } { 20 x y }$ 
D)  $\frac { 20 y + 30 x - 12 x - 15 y } { 4 x + 5 y }$

Question 12

The sum of two numbers is 124. If the larger is divided by the smaller, the quotient is 12 and the remainder is 7. Find the numbers. The larger number is __________, and the smaller number is __________.

Accepted Answer

The answer of The sum of two numbers is 124....

Question 13

Simplify the rational expression. $\frac { 2 x ^ { 2 } + 4 x } { x ^ { 3 } + 8 }$

Accepted Answer

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

Question 14

Simplify the rational expression. $\frac { 64 x ^ { 4 } + 27 x } { 8 x ^ { 3 } - 26 x ^ { 2 } - 24 x }$

Accepted Answer

A)  $\frac { 16 x ^ { 2 } - 24 x + 9 } { 2 x ( x - 4 ) }$ 
B)  $\frac { 16 x ^ { 2 } - 12 x + 9 } { 2 ( x - 4 ) }$ 
C)  $\frac { 16 x ^ { 2 } + 12 x + 9 } { 2 ( x + 4 ) }$ 
D)  $\frac { x \left( 16 x ^ { 2 } - 12 x + 9 \right) } { 2 ( x - 4 ) }$ 
A)  $\frac { 16 x ^ { 2 } - 24 x + 9 } { 2 x ( x - 4 ) }$ 
B)  $\frac { 16 x ^ { 2 } - 12 x + 9 } { 2 ( x - 4 ) }$ 
C)  $\frac { 16 x ^ { 2 } + 12 x + 9 } { 2 ( x + 4 ) }$ 
D)  $\frac { x \left( 16 x ^ { 2 } - 12 x + 9 \right) } { 2 ( x - 4 ) }$

Question 15

Simplify the rational expression. $\frac { 35 x + 28 } { 35 x - 28 }$

Accepted Answer

The answer of Simplify the rational expression. \(\frac { 35...

Question 16

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

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

Question 17

Simplify the complex fraction. $5 + \frac { x } { 5 + \frac { 5 } { x } }$

Accepted Answer

A)  $\frac { x + 25 x + 5 } { 5 ( x + 1 ) }$ 
B)  $\frac { x ^ { 2 } + 25 x + 5 } { 5 ( x + 1 ) }$ 
C)  $\frac { x ^ { 2 } + 25 x + 25 } { 5 ( x + 1 ) }$ 
A)  $\frac { x + 25 x + 5 } { 5 ( x + 1 ) }$ 
B)  $\frac { x ^ { 2 } + 25 x + 5 } { 5 ( x + 1 ) }$ 
C)  $\frac { x ^ { 2 } + 25 x + 25 } { 5 ( x + 1 ) }$

Question 18

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 1 } { 8 } + \frac { 5 } { 9 }$

Accepted Answer

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

Question 19

Subtract the rational expressions. $\frac { 13 } { 14 x } - \frac { 7 } { 10 x }$

Accepted Answer

A)  $\frac { 7 } { 23 x }$ 
B)  $\frac { 8 } { 35 x }$ 
C)  $\frac { 57 } { 35 x }$ 
D)  $\frac { 17 } { 38 x }$ 
A)  $\frac { 7 } { 23 x }$ 
B)  $\frac { 8 } { 35 x }$ 
C)  $\frac { 57 } { 35 x }$ 
D)  $\frac { 17 } { 38 x }$

Question 20

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 5 x } { x - 6 } + \frac { 5 } { x }$ Please enter your answer as one fraction with the denominator factored completely and the numerator not factored.

Accepted Answer

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

Solve the equation. $4 + \frac { 12 } { t - 5 } = \frac { 12 } { t ( t - 5 ) }$

Perform the indicated operation involving rational expressions. Express final answer in reduced form. $\frac { 4 t ^ { 5 } - 8 t ^ { 4 } } { t ^ { 3 } - 9 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 18 t + 81 } { t ^ { 5 } - 4 t ^ { 3 } }$

The perimeter of a rectangle is 266 centimeters. If the ratio of its width to its length is 6 to 13, find the dimensions of the rectangle.

Solve the equation. $\frac { x } { x - 6 } - 2 = \frac { 6 } { x - 6 }$

Simplify the rational expression. $\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x }$

To travel 38 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen to travel 48 miles riding a bicycle. Sue travels 7 miles per hour faster than Doreen. Find the times and rates of both girls.

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 20 minutes?

Uniform motion problems are a special case of a rate-time problem.

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 8 x } - \frac { 6 } { x }$

Simplify the rational expression. $\frac { x ^ { 2 } + 5 x - 14 } { 6 - x - x ^ { 2 } }$

Add or subtract the rational expressions. $\frac { 5 } { 4 x } + \frac { 6 } { 5 y } - 3$

The sum of two numbers is 124. If the larger is divided by the smaller, the quotient is 12 and the remainder is 7. Find the numbers. The larger number is , and the smaller number is .

Simplify the rational expression. $\frac { 2 x ^ { 2 } + 4 x } { x ^ { 3 } + 8 }$

Simplify the rational expression. $\frac { 64 x ^ { 4 } + 27 x } { 8 x ^ { 3 } - 26 x ^ { 2 } - 24 x }$

Simplify the rational expression. $\frac { 35 x + 28 } { 35 x - 28 }$

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

Simplify the complex fraction. $5 + \frac { x } { 5 + \frac { 5 } { x } }$

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 1 } { 8 } + \frac { 5 } { 9 }$

Subtract the rational expressions. $\frac { 13 } { 14 x } - \frac { 7 } { 10 x }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 5 x } { x - 6 } + \frac { 5 } { x }$ Please enter your answer as one fraction with the denominator factored completely and the numerator not factored.

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. 4+12t−5=12t(t−5)4 + \frac { 12 } { t - 5 } = \frac { 12 } { t ( t - 5 ) }4+t−512​=t(t−5)12​

The perimeter of a rectangle is 266 centimeters. If the ratio of its width to its length is 6 to 13, find the dimensions of the rectangle.

Solve the equation. xx−6−2=6x−6\frac { x } { x - 6 } - 2 = \frac { 6 } { x - 6 }x−6x​−2=x−66​

Simplify the rational expression. x2−16x2+4x\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x }x2+4xx2−16​

To travel 38 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen to travel 48 miles riding a bicycle. Sue travels 7 miles per hour faster than Doreen. Find the times and rates of both girls.

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 20 minutes?

Uniform motion problems are a special case of a rate-time problem.

Perform the indicated operation and express your answer in simplest form. 7xx2+8x−6x\frac { 7 x } { x ^ { 2 } + 8 x } - \frac { 6 } { x }x2+8x7x​−x6​

Simplify the rational expression. x2+5x−146−x−x2\frac { x ^ { 2 } + 5 x - 14 } { 6 - x - x ^ { 2 } }6−x−x2x2+5x−14​

Add or subtract the rational expressions. 54x+65y−3\frac { 5 } { 4 x } + \frac { 6 } { 5 y } - 34x5​+5y6​−3

The sum of two numbers is 124. If the larger is divided by the smaller, the quotient is 12 and the remainder is 7. Find the numbers. The larger number is __________, and the smaller number is __________.

Simplify the rational expression. 2x2+4xx3+8\frac { 2 x ^ { 2 } + 4 x } { x ^ { 3 } + 8 }x3+82x2+4x​

Simplify the rational expression. 64x4+27x8x3−26x2−24x\frac { 64 x ^ { 4 } + 27 x } { 8 x ^ { 3 } - 26 x ^ { 2 } - 24 x }8x3−26x2−24x64x4+27x​

Simplify the rational expression. 35x+2835x−28\frac { 35 x + 28 } { 35 x - 28 }35x−2835x+28​

Simplify the complex fraction. 5+x5+5x5 + \frac { x } { 5 + \frac { 5 } { x } }5+5+x5​x​

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. 18+59\frac { 1 } { 8 } + \frac { 5 } { 9 }81​+95​

Subtract the rational expressions. 1314x−710x\frac { 13 } { 14 x } - \frac { 7 } { 10 x }14x13​−10x7​

Add the rational expressions. Be sure to express your answer in simplest form. 5xx−6+5x\frac { 5 x } { x - 6 } + \frac { 5 } { x }x−65x​+x5​ Please enter your answer as one fraction with the denominator factored completely and the numerator not factored.

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. $4 + \frac { 12 } { t - 5 } = \frac { 12 } { t ( t - 5 ) }$

Solve the equation. $\frac { x } { x - 6 } - 2 = \frac { 6 } { x - 6 }$

Simplify the rational expression. $\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x }$

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 8 x } - \frac { 6 } { x }$

Simplify the rational expression. $\frac { x ^ { 2 } + 5 x - 14 } { 6 - x - x ^ { 2 } }$

Add or subtract the rational expressions. $\frac { 5 } { 4 x } + \frac { 6 } { 5 y } - 3$

The sum of two numbers is 124. If the larger is divided by the smaller, the quotient is 12 and the remainder is 7. Find the numbers. The larger number is , and the smaller number is .

Simplify the rational expression. $\frac { 2 x ^ { 2 } + 4 x } { x ^ { 3 } + 8 }$

Simplify the rational expression. $\frac { 64 x ^ { 4 } + 27 x } { 8 x ^ { 3 } - 26 x ^ { 2 } - 24 x }$

Simplify the rational expression. $\frac { 35 x + 28 } { 35 x - 28 }$

Simplify the complex fraction. $5 + \frac { x } { 5 + \frac { 5 } { x } }$

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 1 } { 8 } + \frac { 5 } { 9 }$

Subtract the rational expressions. $\frac { 13 } { 14 x } - \frac { 7 } { 10 x }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 5 x } { x - 6 } + \frac { 5 } { x }$ Please enter your answer as one fraction with the denominator factored completely and the numerator not factored.