Question 1

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 a } { a - 9 } - \frac { 27 } { a - 9 }$

Accepted Answer

A)  9 
B)  3 
C)  $\frac { 3 a - 27 } { a + 9 }$ 
D)  $\frac { 3 a + 27 } { a - 9 }$ 
A)  9 
B)  3 
C)  $\frac { 3 a - 27 } { a + 9 }$ 
D)  $\frac { 3 a + 27 } { a - 9 }$

Question 2

Simplify the rational expression. $\frac { a ^ { 2 } + 13 a + 40 } { a ^ { 2 } - 3 a - 40 }$

Accepted Answer

A)  $\frac { a + 8 } { a - 5 }$ 
B)  a + 5 
C)  $\frac { a + 8 } { a + 5 }$ 
D)  $\frac { a + 8 } { a - 8 }$ 
A)  $\frac { a + 8 } { a - 5 }$ 
B)  a + 5 
C)  $\frac { a + 8 } { a + 5 }$ 
D)  $\frac { a + 8 } { a - 8 }$

Question 3

Add or subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 } { 2 m } + \frac { 4 } { 3 n } - 3$

Accepted Answer

A)  $\frac { 9 n + 8 m - m n } { 6 m n }$ 
B)  $\frac { 6 n + 12 m - 6 m - 9 n } { 2 m + 3 n }$ 
C)  $\frac { 9 n + 8 m } { 6 m n }$ 
D)  $\frac { 9 n + 8 m } { 2 m + 3 n } - 3$ 
E)  $\frac { 9 n + 8 m - 18 m n } { 6 m n }$ 
A)  $\frac { 9 n + 8 m - m n } { 6 m n }$ 
B)  $\frac { 6 n + 12 m - 6 m - 9 n } { 2 m + 3 n }$ 
C)  $\frac { 9 n + 8 m } { 6 m n }$ 
D)  $\frac { 9 n + 8 m } { 2 m + 3 n } - 3$ 
E)  $\frac { 9 n + 8 m - 18 m n } { 6 m n }$

Question 4

Solve the equation. $\frac { n } { 2 } = \frac { 3 } { n - 1 }$

Accepted Answer

A)  $\{ 2 , - 6 \}$ 
B)  $\{ - 2,6 \}$ 
C)  $\{ - 2,3 \}$ 
D)  $\{ 2 , - 3 \}$ 
E)  $\{ 2,3 \}$ 
A)  $\{ 2 , - 6 \}$ 
B)  $\{ - 2,6 \}$ 
C)  $\{ - 2,3 \}$ 
D)  $\{ 2 , - 3 \}$ 
E)  $\{ 2,3 \}$

Question 5

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 } { 5 x + 2 } + \frac { 5 } { 3 x + 7 }$

Accepted Answer

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

Question 6

Solve the equation. $\frac { 5 } { 6 x } + \frac { 4 } { 5 } = \frac { 5 } { 4 x }$

Accepted Answer

The answer of Solve the equation. \(\frac { 5 }...

Question 7

Solve the equation. $\frac { x + 1 } { 6 } + \frac { x - 4 } { 6 } = \frac { 5 } { 6 }$

Accepted Answer

A)  x = 1 
B)  x = -1 
C)  x = 4 
D)  x = 8 
E)  x = 6 
A)  x = 1 
B)  x = -1 
C)  x = 4 
D)  x = 8 
E)  x = 6

Question 8

Felipe jogs for 15 miles and then walks another 15 miles. He jogs $3 \frac { 1 } { 2 }$ miles per hour faster than he walks, and the entire distance of 30 miles takes 8.5 hours. Find the rate at which he walks and the rate at which he jogs. __________ mph jogging __________ mph walking

Accepted Answer

The answer of Felipe jogs for 15 miles and then...

Question 9

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 2 a } { a - 3 } - \frac { 6 } { a - 3 }$

Accepted Answer

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

Question 10

In solving a rational equation, all possible answers must be checked in the original equation.

Accepted Answer

A) True 
 B)False

Question 11

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 24 n - 36 - 4 n ^ { 2 } } { 50 n - 125 - 5 n ^ { 2 } } \cdot \frac { 350 n - 875 - 35 n ^ { 2 } } { 512 - 256 n + 32 n ^ { 2 } }$

Accepted Answer

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

Question 12

Solve the equation. $\frac { 5 y - 91 } { 10 y ^ { 2 } + 11 y - 6 } - \frac { 3 } { 2 y + 3 } = \frac { 5 } { 5 y - 2 }$

Accepted Answer

A)  y = 5 
B)  y = -5 
C)  y = 0 
A)  y = 5 
B)  y = -5 
C)  y = 0

Question 13

An inlet pipe can fill a tank in 7 hours, and a drain pipe can empty the same tank in 9 hours. If the drain is left open while filling the tank, it would take 16 hours to fill the tank.

Accepted Answer

A) True 
 B)False

Question 14

Perform the indicated operation involving rational expressions. $\frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 6 t + 9 } { t ^ { 5 } - 9 t ^ { 3 } }$

Accepted Answer

A)  $\frac { 7 t - 21 } { t ^ { 2 } + 3 t }$ 
B)  $\frac { t - 3 } { t ^ { 2 } + 3 t }$ 
C)  $\frac { 7 } { t ^ { 2 } + 3 t }$ 
D)  $\frac { 7 t ^ { 2 } + 21 } { t ^ { 2 } + 3 t }$ 
A)  $\frac { 7 t - 21 } { t ^ { 2 } + 3 t }$ 
B)  $\frac { t - 3 } { t ^ { 2 } + 3 t }$ 
C)  $\frac { 7 } { t ^ { 2 } + 3 t }$ 
D)  $\frac { 7 t ^ { 2 } + 21 } { t ^ { 2 } + 3 t }$

Question 15

Perform the indicated operation and express your answer in simplest form. $\frac { x } { x ^ { 2 } - 1 } + \frac { 6 } { x - 1 }$ 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 16

The multiplication identity property is used to make equivalent fractions.

Accepted Answer

A) True 
 B)False

Question 17

Solve the equation for the variable N . $F = \frac { 400 N } { C }$

Accepted Answer

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

Question 18

Solve the equation. $\frac { x + 2 } { 2 } - \frac { x - 3 } { 5 } = 1$

Accepted Answer

A)  x = $-$ 3 
B)  x = $-$ 2 
C)  x = $-$ 0 
D)  x = $-$ 4 
E)  x = $-$ 6 
A)  x = $-$ 3 
B)  x = $-$ 2 
C)  x = $-$ 0 
D)  x = $-$ 4 
E)  x = $-$ 6

Question 19

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 7 } { 3 x ^ { 2 } } - \frac { 17 } { 8 x } - \frac { 9 } { 4 x }$

Accepted Answer

A)  $\frac { 56 - 105 x } { 24 x ^ { 2 } }$ 
B)  $\frac { 56 - 3 x } { 24 x ^ { 2 } }$ 
C)  $\frac { 56 + 3 x } { 24 x }$ 
D)  $\frac { 56 + 3 x } { 24 x ^ { 2 } }$ 
A)  $\frac { 56 - 105 x } { 24 x ^ { 2 } }$ 
B)  $\frac { 56 - 3 x } { 24 x ^ { 2 } }$ 
C)  $\frac { 56 + 3 x } { 24 x }$ 
D)  $\frac { 56 + 3 x } { 24 x ^ { 2 } }$

Question 20

Solve the equation. $\frac { n } { 75 - n } = 4 + \frac { 50 } { 75 - n }$

Accepted Answer

A)  n = 68 
B)  n = 73 
C)  n = 70 
D)  n = 66 
E)  n = 71 
A)  n = 68 
B)  n = 73 
C)  n = 70 
D)  n = 66 
E)  n = 71

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 a } { a - 9 } - \frac { 27 } { a - 9 }$

Simplify the rational expression. $\frac { a ^ { 2 } + 13 a + 40 } { a ^ { 2 } - 3 a - 40 }$

Add or subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 } { 2 m } + \frac { 4 } { 3 n } - 3$

Solve the equation. $\frac { n } { 2 } = \frac { 3 } { n - 1 }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 } { 5 x + 2 } + \frac { 5 } { 3 x + 7 }$

Solve the equation. $\frac { 5 } { 6 x } + \frac { 4 } { 5 } = \frac { 5 } { 4 x }$

Solve the equation. $\frac { x + 1 } { 6 } + \frac { x - 4 } { 6 } = \frac { 5 } { 6 }$

Felipe jogs for 15 miles and then walks another 15 miles. He jogs $3 \frac { 1 } { 2 }$ miles per hour faster than he walks, and the entire distance of 30 miles takes 8.5 hours. Find the rate at which he walks and the rate at which he jogs. mph jogging mph walking

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 2 a } { a - 3 } - \frac { 6 } { a - 3 }$

In solving a rational equation, all possible answers must be checked in the original equation.

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 24 n - 36 - 4 n ^ { 2 } } { 50 n - 125 - 5 n ^ { 2 } } \cdot \frac { 350 n - 875 - 35 n ^ { 2 } } { 512 - 256 n + 32 n ^ { 2 } }$

Solve the equation. $\frac { 5 y - 91 } { 10 y ^ { 2 } + 11 y - 6 } - \frac { 3 } { 2 y + 3 } = \frac { 5 } { 5 y - 2 }$

An inlet pipe can fill a tank in 7 hours, and a drain pipe can empty the same tank in 9 hours. If the drain is left open while filling the tank, it would take 16 hours to fill the tank.

Perform the indicated operation involving rational expressions. $\frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 6 t + 9 } { t ^ { 5 } - 9 t ^ { 3 } }$

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

The multiplication identity property is used to make equivalent fractions.

Solve the equation for the variable N . $F = \frac { 400 N } { C }$

Solve the equation. $\frac { x + 2 } { 2 } - \frac { x - 3 } { 5 } = 1$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 7 } { 3 x ^ { 2 } } - \frac { 17 } { 8 x } - \frac { 9 } { 4 x }$

Solve the equation. $\frac { n } { 75 - n } = 4 + \frac { 50 } { 75 - n }$

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

Subtract the rational expressions. Be sure to express your answer in simplest form. 3aa−9−27a−9\frac { 3 a } { a - 9 } - \frac { 27 } { a - 9 }a−93a​−a−927​

Simplify the rational expression. a2+13a+40a2−3a−40\frac { a ^ { 2 } + 13 a + 40 } { a ^ { 2 } - 3 a - 40 }a2−3a−40a2+13a+40​

Add or subtract the rational expressions. Be sure to express your answer in simplest form. 32m+43n−3\frac { 3 } { 2 m } + \frac { 4 } { 3 n } - 32m3​+3n4​−3

Solve the equation. n2=3n−1\frac { n } { 2 } = \frac { 3 } { n - 1 }2n​=n−13​

Add the rational expressions. Be sure to express your answer in simplest form. 35x+2+53x+7\frac { 3 } { 5 x + 2 } + \frac { 5 } { 3 x + 7 }5x+23​+3x+75​

Solve the equation. 56x+45=54x\frac { 5 } { 6 x } + \frac { 4 } { 5 } = \frac { 5 } { 4 x }6x5​+54​=4x5​

Solve the equation. x+16+x−46=56\frac { x + 1 } { 6 } + \frac { x - 4 } { 6 } = \frac { 5 } { 6 }6x+1​+6x−4​=65​

Felipe jogs for 15 miles and then walks another 15 miles. He jogs 3123 \frac { 1 } { 2 }321​ miles per hour faster than he walks, and the entire distance of 30 miles takes 8.5 hours. Find the rate at which he walks and the rate at which he jogs. __________ mph jogging __________ mph walking

Subtract the rational expressions. Be sure to express your answer in simplest form. 2aa−3−6a−3\frac { 2 a } { a - 3 } - \frac { 6 } { a - 3 }a−32a​−a−36​

In solving a rational equation, all possible answers must be checked in the original equation.

Solve the equation. 5y−9110y2+11y−6−32y+3=55y−2\frac { 5 y - 91 } { 10 y ^ { 2 } + 11 y - 6 } - \frac { 3 } { 2 y + 3 } = \frac { 5 } { 5 y - 2 }10y2+11y−65y−91​−2y+33​=5y−25​

An inlet pipe can fill a tank in 7 hours, and a drain pipe can empty the same tank in 9 hours. If the drain is left open while filling the tank, it would take 16 hours to fill the tank.

Perform the indicated operation involving rational expressions. 7t5−21t4t3−3t2⋅t2−6t+9t5−9t3\frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 6 t + 9 } { t ^ { 5 } - 9 t ^ { 3 } }t3−3t27t5−21t4​⋅t5−9t3t2−6t+9​

Perform the indicated operation and express your answer in simplest form. xx2−1+6x−1\frac { x } { x ^ { 2 } - 1 } + \frac { 6 } { x - 1 }x2−1x​+x−16​ Please enter your answer as one fraction with the denominator factored completely.

The multiplication identity property is used to make equivalent fractions.

Solve the equation for the variable N . F=400NCF = \frac { 400 N } { C }F=C400N​

Solve the equation. x+22−x−35=1\frac { x + 2 } { 2 } - \frac { x - 3 } { 5 } = 12x+2​−5x−3​=1

Subtract the rational expressions. Be sure to express your answer in simplest form. 73x2−178x−94x\frac { 7 } { 3 x ^ { 2 } } - \frac { 17 } { 8 x } - \frac { 9 } { 4 x }3x27​−8x17​−4x9​

Solve the equation. n75−n=4+5075−n\frac { n } { 75 - n } = 4 + \frac { 50 } { 75 - n }75−nn​=4+75−n50​

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

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 a } { a - 9 } - \frac { 27 } { a - 9 }$

Simplify the rational expression. $\frac { a ^ { 2 } + 13 a + 40 } { a ^ { 2 } - 3 a - 40 }$

Add or subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 } { 2 m } + \frac { 4 } { 3 n } - 3$

Solve the equation. $\frac { n } { 2 } = \frac { 3 } { n - 1 }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 } { 5 x + 2 } + \frac { 5 } { 3 x + 7 }$

Solve the equation. $\frac { 5 } { 6 x } + \frac { 4 } { 5 } = \frac { 5 } { 4 x }$

Solve the equation. $\frac { x + 1 } { 6 } + \frac { x - 4 } { 6 } = \frac { 5 } { 6 }$

Felipe jogs for 15 miles and then walks another 15 miles. He jogs $3 \frac { 1 } { 2 }$ miles per hour faster than he walks, and the entire distance of 30 miles takes 8.5 hours. Find the rate at which he walks and the rate at which he jogs. mph jogging mph walking

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 2 a } { a - 3 } - \frac { 6 } { a - 3 }$

Solve the equation. $\frac { 5 y - 91 } { 10 y ^ { 2 } + 11 y - 6 } - \frac { 3 } { 2 y + 3 } = \frac { 5 } { 5 y - 2 }$

Perform the indicated operation involving rational expressions. $\frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 6 t + 9 } { t ^ { 5 } - 9 t ^ { 3 } }$

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

Solve the equation for the variable N . $F = \frac { 400 N } { C }$

Solve the equation. $\frac { x + 2 } { 2 } - \frac { x - 3 } { 5 } = 1$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 7 } { 3 x ^ { 2 } } - \frac { 17 } { 8 x } - \frac { 9 } { 4 x }$

Solve the equation. $\frac { n } { 75 - n } = 4 + \frac { 50 } { 75 - n }$