Question 1

Solve the equation. $n - \frac { 15 } { n } = \frac { 103 } { 6 }$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 6 } , 18 \right\}$ 
B)  $\left\{ - \frac { 5 } { 6 } \right\}$ 
C)  $\{ 18 \}$ 
D)  $\left\{ - \frac { 7 } { 6 } \right\}$ 
E)  $\left\{ - \frac { 5 } { 6 } , 18 \right\}$ 
A)  $\left\{ - \frac { 7 } { 6 } , 18 \right\}$ 
B)  $\left\{ - \frac { 5 } { 6 } \right\}$ 
C)  $\{ 18 \}$ 
D)  $\left\{ - \frac { 7 } { 6 } \right\}$ 
E)  $\left\{ - \frac { 5 } { 6 } , 18 \right\}$ E

Question 2

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 17 } { 18 x } - \frac { 1 } { 10 x }$

Accepted Answer

$\frac { 38 } { 45 x }$

Question 3

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 11 } { 12 x ^ { 2 } y } - \frac { 5 x } { 6 y ^ { 2 } }$

Accepted Answer

$\frac { 11 y - 10 x ^ { 3 } } { 12 x ^ { 2 } y ^ { 2 } }$

Question 4

Perform the indicated operation involving rational numbers. Express final answer in reduced form. $\frac { 3 } { - 4 } \cdot \frac { - 12 } { 39 }$

Accepted Answer

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

Question 5

Perform the indicated operations involving rational numbers. Match each expression with the corresponding answer.
-$\frac { 1 } { 6 }$

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 6

Felipe jogs for 12 miles and then walks another 12 miles. He jogs $2 \frac { 1 } { 2 }$ miles per hour faster than he walks, and the entire distance of 24 miles takes 11 hours. Find the rate at which he walks and the rate at which he jogs.

Accepted Answer

A)  Jog at 4 mph and walk at 2 mph. 
B)  Jog at 4.5 mph and walk at 2 mph. 
C)  Jog at 4 mph and walk at 1.5 mph. 
A)  Jog at 4 mph and walk at 2 mph. 
B)  Jog at 4.5 mph and walk at 2 mph. 
C)  Jog at 4 mph and walk at 1.5 mph.

Question 7

Simplify the rational expression. $\frac { 5 y ^ { 2 } + 49 y + 36 } { 25 y ^ { 2 } - 16 }$

Accepted Answer

The answer of Simplify the rational expression. \(\frac { 5...

Question 8

Perform the indicated operation and express your answer in simplest form. $\frac { 5 } { x ^ { 2 } + 3 } - \frac { 2 } { x ^ { 2 } - 4 x - 5 }$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } + 3 \right) ( x - 1 ) ( x + 5 ) }$ 
B)  $\frac { x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } + 3 \right) ( x - 1 ) ( x + 5 ) }$ 
C)  $\frac { x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } + 3 \right) ( x + 1 ) ( x - 5 ) }$ 
D)  $\frac { x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } - 3 \right) ( x + 1 ) ( x - 5 ) }$ 
E)  $\frac { 3 x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } + 3 \right) ( x + 1 ) ( x - 5 ) }$ 
A)  $\frac { 3 x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } + 3 \right) ( x - 1 ) ( x + 5 ) }$ 
B)  $\frac { x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } + 3 \right) ( x - 1 ) ( x + 5 ) }$ 
C)  $\frac { x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } + 3 \right) ( x + 1 ) ( x - 5 ) }$ 
D)  $\frac { x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } - 3 \right) ( x + 1 ) ( x - 5 ) }$ 
E)  $\frac { 3 x ^ { 2 } - 20 x - 31 } { \left( x ^ { 2 } + 3 \right) ( x + 1 ) ( x - 5 ) }$

Question 9

In rational expressions, the variables are restricted to exclude division by zero.

Accepted Answer

A) True 
 B)False

Question 10

Simplify the rational expression. $\frac { 25 x y } { 35 y }$

Accepted Answer

A)  $\frac { 5 x y } { 7 }$ 
B)  $\frac { 5 x } { 7 }$ 
C)  $\frac { x } { 2 }$ 
D)  $\frac { 1 } { 2 x }$ 
A)  $\frac { 5 x y } { 7 }$ 
B)  $\frac { 5 x } { 7 }$ 
C)  $\frac { x } { 2 }$ 
D)  $\frac { 1 } { 2 x }$

Question 11

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 4 x } { x - 4 } + \frac { 2 } { x }$

Accepted Answer

A)  $\frac { 6 x - 8 } { x ( x - 4 ) }$ 
B)  $\frac { 4 x ^ { 2 } + 2 x + 8 } { x ^ { 2 } - 5 x }$ 
C)  $\frac { 4 x ^ { 2 } + 2 x - 8 } { x ( x - 4 ) }$ 
D)  $\frac { 4 x ^ { 2 } + 2 x + 8 } { x ( x - 4 ) }$ 
A)  $\frac { 6 x - 8 } { x ( x - 4 ) }$ 
B)  $\frac { 4 x ^ { 2 } + 2 x + 8 } { x ^ { 2 } - 5 x }$ 
C)  $\frac { 4 x ^ { 2 } + 2 x - 8 } { x ( x - 4 ) }$ 
D)  $\frac { 4 x ^ { 2 } + 2 x + 8 } { x ( x - 4 ) }$

Question 12

The least common denominator of the rational expressions in a rational equation is the product of the denominators.

Accepted Answer

A) True 
 B)False

Question 13

Perform the indicated operations involving rational numbers. Express the final answer in reduced form. $\frac { 4 } { 9 } \cdot \frac { 6 } { 17 } \div \frac { 1 } { 6 }$

Accepted Answer

A)  $\frac { 1 } { 18 }$ 
B)  $\frac { 17 } { 18 }$ 
C)  $\frac { 16 } { 17 }$ 
D)  $\frac { 1 } { 17 }$ 
E)  $1$ 
A)  $\frac { 1 } { 18 }$ 
B)  $\frac { 17 } { 18 }$ 
C)  $\frac { 16 } { 17 }$ 
D)  $\frac { 1 } { 17 }$ 
E)  $1$

Question 14

Perform the indicated operation and express your answer in simplest form. $$\frac { n } { n - 3 } + \frac { n + 7 } { n + 7 } + \frac { 16 n + 21 } { n ^ { 2 } + 4 n - 21 }$$ 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 15

Solve each equation for the variable x . $y = \frac { 2 } { 3 } x + \frac { 5 } { 18 }$

Accepted Answer

A)  $x = \frac { 3 } { 2 } y - \frac { 5 } { 12 }$ 
B)  $x = - \frac { 3 } { 2 } y + \frac { 5 } { 12 }$ 
C)  $x = \frac { 3 } { 2 } y + \frac { 5 } { 2 }$ 
A)  $x = \frac { 3 } { 2 } y - \frac { 5 } { 12 }$ 
B)  $x = - \frac { 3 } { 2 } y + \frac { 5 } { 12 }$ 
C)  $x = \frac { 3 } { 2 } y + \frac { 5 } { 2 }$

Question 16

Simplify the rational expression. $\frac { 24 x y } { 54 y }$

Accepted Answer

The answer of Simplify the rational expression. \(\frac { 24...

Question 17

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 7 x } { x - 4 } - 6$

Accepted Answer

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

Question 18

Recall that the indicated quotient of a polynomial and its opposite is $-$ 1. For example, $\frac { x - 2 } { 2 - x }$ simplifies to $-$ 1. Keep this idea in mind as you add or subtract the following rational expression. $\frac { 2 } { x - 2 } - \frac { x } { x - 2 } + 4$

Accepted Answer

The answer of Recall that the indicated quotient of a...

Question 19

Besides setting the cross products equal to each other in order to solve the equation $\frac { H } { p } = \frac { W } { \rho + W }$ for P , the distributive property will also be used in the process to isolate P .

Accepted Answer

A) True 
 B)False

Question 20

The first step in adding rational expressions is to reduce the fractions.

Accepted Answer

A) True 
 B)False

Solve the equation. $n - \frac { 15 } { n } = \frac { 103 } { 6 }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 17 } { 18 x } - \frac { 1 } { 10 x }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 11 } { 12 x ^ { 2 } y } - \frac { 5 x } { 6 y ^ { 2 } }$

Perform the indicated operation involving rational numbers. Express final answer in reduced form. $\frac { 3 } { - 4 } \cdot \frac { - 12 } { 39 }$

Perform the indicated operations involving rational numbers. Match each expression with the corresponding answer. - $\frac { 1 } { 6 }$

Felipe jogs for 12 miles and then walks another 12 miles. He jogs $2 \frac { 1 } { 2 }$ miles per hour faster than he walks, and the entire distance of 24 miles takes 11 hours. Find the rate at which he walks and the rate at which he jogs.

Simplify the rational expression. $\frac { 5 y ^ { 2 } + 49 y + 36 } { 25 y ^ { 2 } - 16 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 5 } { x ^ { 2 } + 3 } - \frac { 2 } { x ^ { 2 } - 4 x - 5 }$

In rational expressions, the variables are restricted to exclude division by zero.

Simplify the rational expression. $\frac { 25 x y } { 35 y }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 4 x } { x - 4 } + \frac { 2 } { x }$

The least common denominator of the rational expressions in a rational equation is the product of the denominators.

Perform the indicated operations involving rational numbers. Express the final answer in reduced form. $\frac { 4 } { 9 } \cdot \frac { 6 } { 17 } \div \frac { 1 } { 6 }$

Perform the indicated operation and express your answer in simplest form. $\frac { n } { n - 3 } + \frac { n + 7 } { n + 7 } + \frac { 16 n + 21 } { n ^ { 2 } + 4 n - 21 }$ Please enter your answer as one fraction with the denominator factored completely.

Solve each equation for the variable x . $y = \frac { 2 } { 3 } x + \frac { 5 } { 18 }$

Simplify the rational expression. $\frac { 24 x y } { 54 y }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 7 x } { x - 4 } - 6$

Recall that the indicated quotient of a polynomial and its opposite is $-$ 1. For example, $\frac { x - 2 } { 2 - x }$ simplifies to $-$ 1. Keep this idea in mind as you add or subtract the following rational expression. $\frac { 2 } { x - 2 } - \frac { x } { x - 2 } + 4$

Besides setting the cross products equal to each other in order to solve the equation $\frac { H } { p } = \frac { W } { \rho + W }$ for P , the distributive property will also be used in the process to isolate P .

The first step in adding rational expressions is to reduce the fractions.

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. n−15n=1036n - \frac { 15 } { n } = \frac { 103 } { 6 }n−n15​=6103​

Subtract the rational expressions. Be sure to express your answer in simplest form. 1718x−110x\frac { 17 } { 18 x } - \frac { 1 } { 10 x }18x17​−10x1​

Subtract the rational expressions. Be sure to express your answer in simplest form. 1112x2y−5x6y2\frac { 11 } { 12 x ^ { 2 } y } - \frac { 5 x } { 6 y ^ { 2 } }12x2y11​−6y25x​

Perform the indicated operation involving rational numbers. Express final answer in reduced form. 3−4⋅−1239\frac { 3 } { - 4 } \cdot \frac { - 12 } { 39 }−43​⋅39−12​

Perform the indicated operations involving rational numbers. Match each expression with the corresponding answer. - 16\frac { 1 } { 6 }61​

Felipe jogs for 12 miles and then walks another 12 miles. He jogs 2122 \frac { 1 } { 2 }221​ miles per hour faster than he walks, and the entire distance of 24 miles takes 11 hours. Find the rate at which he walks and the rate at which he jogs.

Simplify the rational expression. 5y2+49y+3625y2−16\frac { 5 y ^ { 2 } + 49 y + 36 } { 25 y ^ { 2 } - 16 }25y2−165y2+49y+36​

Perform the indicated operation and express your answer in simplest form. 5x2+3−2x2−4x−5\frac { 5 } { x ^ { 2 } + 3 } - \frac { 2 } { x ^ { 2 } - 4 x - 5 }x2+35​−x2−4x−52​

In rational expressions, the variables are restricted to exclude division by zero.

Simplify the rational expression. 25xy35y\frac { 25 x y } { 35 y }35y25xy​

Add the rational expressions. Be sure to express your answer in simplest form. 4xx−4+2x\frac { 4 x } { x - 4 } + \frac { 2 } { x }x−44x​+x2​

The least common denominator of the rational expressions in a rational equation is the product of the denominators.

Perform the indicated operations involving rational numbers. Express the final answer in reduced form. 49⋅617÷16\frac { 4 } { 9 } \cdot \frac { 6 } { 17 } \div \frac { 1 } { 6 }94​⋅176​÷61​

Solve each equation for the variable x . y=23x+518y = \frac { 2 } { 3 } x + \frac { 5 } { 18 }y=32​x+185​

Simplify the rational expression. 24xy54y\frac { 24 x y } { 54 y }54y24xy​

Subtract the rational expressions. Be sure to express your answer in simplest form. 7xx−4−6\frac { 7 x } { x - 4 } - 6x−47x​−6

Besides setting the cross products equal to each other in order to solve the equation Hp=Wρ+W\frac { H } { p } = \frac { W } { \rho + W }pH​=ρ+WW​ for P , the distributive property will also be used in the process to isolate P .

The first step in adding rational expressions is to reduce the fractions.

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. $n - \frac { 15 } { n } = \frac { 103 } { 6 }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 17 } { 18 x } - \frac { 1 } { 10 x }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 11 } { 12 x ^ { 2 } y } - \frac { 5 x } { 6 y ^ { 2 } }$

Perform the indicated operation involving rational numbers. Express final answer in reduced form. $\frac { 3 } { - 4 } \cdot \frac { - 12 } { 39 }$

Perform the indicated operations involving rational numbers. Match each expression with the corresponding answer. - $\frac { 1 } { 6 }$

Felipe jogs for 12 miles and then walks another 12 miles. He jogs $2 \frac { 1 } { 2 }$ miles per hour faster than he walks, and the entire distance of 24 miles takes 11 hours. Find the rate at which he walks and the rate at which he jogs.

Simplify the rational expression. $\frac { 5 y ^ { 2 } + 49 y + 36 } { 25 y ^ { 2 } - 16 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 5 } { x ^ { 2 } + 3 } - \frac { 2 } { x ^ { 2 } - 4 x - 5 }$

Simplify the rational expression. $\frac { 25 x y } { 35 y }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 4 x } { x - 4 } + \frac { 2 } { x }$

Perform the indicated operations involving rational numbers. Express the final answer in reduced form. $\frac { 4 } { 9 } \cdot \frac { 6 } { 17 } \div \frac { 1 } { 6 }$

Solve each equation for the variable x . $y = \frac { 2 } { 3 } x + \frac { 5 } { 18 }$

Simplify the rational expression. $\frac { 24 x y } { 54 y }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 7 x } { x - 4 } - 6$

Besides setting the cross products equal to each other in order to solve the equation $\frac { H } { p } = \frac { W } { \rho + W }$ for P , the distributive property will also be used in the process to isolate P .