Question 1

Add the rational expressions. $\frac { 2 x } { x - 7 } + \frac { 16 } { x - 7 }$

Accepted Answer

A)  $\frac { 2 x + 9 } { x - 7 }$ 
B)  $\frac { 2 x + 16 } { x - 7 }$ 
C)  $\frac { 2 x - 8 } { x + 7 }$ 
D)  $\frac { 2 x - 8 } { x - 7 }$ 
A)  $\frac { 2 x + 9 } { x - 7 }$ 
B)  $\frac { 2 x + 16 } { x - 7 }$ 
C)  $\frac { 2 x - 8 } { x + 7 }$ 
D)  $\frac { 2 x - 8 } { x - 7 }$

Question 2

Perform the indicated operations involving rational expressions. Match each expression with the corresponding answer.
-$- \frac { x ^ { 3 } } { 56 y ^ { 2 } }$

Accepted Answer

A)  $\frac { 3 x y } { 32 y ^ { 4 } } \cdot \frac { 4 x ^ { 3 } y } { - 21 x }$ 
B)  $\frac { - 3 x y ^ { 4 } } { 4 y ^ { 2 } } \cdot \frac { 28 x ^ { 2 } y ^ { 3 } } { 24 y ^ { 2 } }$ 
A)  $\frac { 3 x y } { 32 y ^ { 4 } } \cdot \frac { 4 x ^ { 3 } y } { - 21 x }$ 
B)  $\frac { - 3 x y ^ { 4 } } { 4 y ^ { 2 } } \cdot \frac { 28 x ^ { 2 } y ^ { 3 } } { 24 y ^ { 2 } }$

Question 3

Solve each equation. Match each equation with the corresponding solution.
-$n = 0.75$

Accepted Answer

A)  $\frac { 5 } { n + 3 } + \frac { 4 } { n - 4 } = \frac { 5 n - 1 } { n ^ { 2 } - n - 12 }$ 
B)  $\frac { 4 } { n + 4 } + \frac { 4 } { n - 5 } = \frac { 4 n - 1 } { n ^ { 2 } - n - 20 }$ 
A)  $\frac { 5 } { n + 3 } + \frac { 4 } { n - 4 } = \frac { 5 n - 1 } { n ^ { 2 } - n - 12 }$ 
B)  $\frac { 4 } { n + 4 } + \frac { 4 } { n - 5 } = \frac { 4 n - 1 } { n ^ { 2 } - n - 20 }$

Question 4

One angle of a triangle has a measure of $75 ^ { \circ }$ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles.

Accepted Answer

A)  $42 ^ { \circ }$ and $63 ^ { \circ }$ 
B)  $44 ^ { \circ }$ and $61 ^ { \circ }$ 
C)  $46 ^ { \circ }$ and $61 ^ { \circ }$ 
D)  $44 ^ { \circ }$ and $590$ 
E)  $46 ^ { \circ }$ and $590$ 
A)  $42 ^ { \circ }$ and $63 ^ { \circ }$ 
B)  $44 ^ { \circ }$ and $61 ^ { \circ }$ 
C)  $46 ^ { \circ }$ and $61 ^ { \circ }$ 
D)  $44 ^ { \circ }$ and $590$ 
E)  $46 ^ { \circ }$ and $590$

Question 5

Kent drives his Mazda 250 miles in the same time that Dave drives his Nissan 225 miles. If Kent averages 5 miles per hour faster than Dave, find their rates.

Accepted Answer

A)  50 mph for Dave and 40 mph for Kent 
B)  45 mph for Dave and 50 mph for Kent 
C)  40 mph for Dave and 45 mph for Kent 
A)  50 mph for Dave and 40 mph for Kent 
B)  45 mph for Dave and 50 mph for Kent 
C)  40 mph for Dave and 45 mph for Kent

Question 6

Solve the equation. $n - \frac { 2 } { n } = \frac { 7 } { 2 }$

Accepted Answer

The answer of Solve the equation. \(n - \frac {...

Question 7

If two inlet pipes are both open, they can fill a pool in 2 hours and 24 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? __________ hours

Accepted Answer

The answer of If two inlet pipes are both open,...

Question 8

Perform the indicated operation. $\frac { 27 } { x ^ { 2 } - 4 x - 21 } - \frac { 4 } { x ^ { 2 } - 6 x - 7 }$

Accepted Answer

A)  $\frac { 23 x + 15 } { ( x - 7 ) ( x + 3 ) ( x - 1 ) }$ 
B)  $\frac { 23 x + 15 } { ( x - 7 ) ( x + 3 ) ( x + 1 ) }$ 
C)  $\frac { 23 x + 15 } { ( x - 7 ) ( x - 3 ) ( x + 1 ) }$ 
D)  No correct answer. 
A)  $\frac { 23 x + 15 } { ( x - 7 ) ( x + 3 ) ( x - 1 ) }$ 
B)  $\frac { 23 x + 15 } { ( x - 7 ) ( x + 3 ) ( x + 1 ) }$ 
C)  $\frac { 23 x + 15 } { ( x - 7 ) ( x - 3 ) ( x + 1 ) }$ 
D)  No correct answer.

Question 9

Solve the equation. $5 + \frac { 25 } { n - 5 } = \frac { 125 } { n ^ { 2 } - 5 n }$

Accepted Answer

A)  n = 1 
B)  n = -5 
C)  n = 5 
A)  n = 1 
B)  n = -5 
C)  n = 5

Question 10

Solve the equation. $\frac { x } { 4 x ^ { 2 } + 6 x } - \frac { x } { 4 x ^ { 2 } + 10 x + 6 } = \frac { 3 } { x ^ { 2 } + x }$

Accepted Answer

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

Question 11

An inlet pipe can fill a tank in 15 minutes. A drain can empty the tank in 20 minutes. If the tank is empty and both the pipe and drain are open, how long will it take before the tank overflows?   __________ minutes

Accepted Answer

The answer of An inlet pipe can fill a tank...

Question 12

Solve the equation. $\frac { a } { a + 1 } - 7 = \frac { 8 a } { a + 1 }$

Accepted Answer

A)  $\{ - 1 \}$ 
B)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 2 } \right\}$ 
A)  $\{ - 1 \}$ 
B)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 2 } \right\}$

Question 13

Solve the equation. $\frac { 5 } { n } + \frac { 1 } { 4 } = \frac { 13 } { 2 n }$

Accepted Answer

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

Question 14

Perform the indicated operations involving rational expressions. Express the final answer in simplest form. $\frac { 6 n ^ { 2 } + 30 n - 36 } { 3 n ^ { 2 } + 10 n - 48 } \cdot \frac { 6 n ^ { 2 } - n - 40 } { 10 n ^ { 2 } + 15 n - 25 }$

Accepted Answer

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

Question 15

Simplify the rational expression. $\frac { 28 x ^ { 3 } z } { - 30 x y z ^ { 2 } }$

Accepted Answer

The answer of Simplify the rational expression. \(\frac { 28...

Question 16

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

Accepted Answer

A)  $- \frac { 4 } { x - 1 }$ 
B)  $- \frac { 4 y } { x + y }$ 
C)  $- \frac { 4 } { x + 1 }$ 
D)  $- \frac { 4 y } { x + 1 }$ 
E)  $- \frac { 4 } { x + y }$ 
A)  $- \frac { 4 } { x - 1 }$ 
B)  $- \frac { 4 y } { x + y }$ 
C)  $- \frac { 4 } { x + 1 }$ 
D)  $- \frac { 4 y } { x + 1 }$ 
E)  $- \frac { 4 } { x + y }$

Question 17

To simplify a rational expression, divide out any common terms.

Accepted Answer

A) True 
 B)False

Question 18

The ratio of male students to female students at a certain university is 3 to 2. If there is a total of 5,000 students, find the number of male students and the number of female students.

Accepted Answer

A)  There are 2,800 male students and 2,200 female students. 
B)  There are 3,100 male students and 1,900 female students. 
C)  There are 2,500 male students and 2,500 female students. 
D)  There are 3,000 male students and 2,000 female students. 
E)  There are 2,700 male students and 2,300 female students. 
A)  There are 2,800 male students and 2,200 female students. 
B)  There are 3,100 male students and 1,900 female students. 
C)  There are 2,500 male students and 2,500 female students. 
D)  There are 3,000 male students and 2,000 female students. 
E)  There are 2,700 male students and 2,300 female students.

Question 19

One angle of a triangle has a measure of $65 ^ { \circ }$ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles. __________ and __________

Accepted Answer

The answer of One angle of a triangle has a...

Question 20

Simplify the rational expression. $\frac { x y + c y + k x + c k } { x y + c y + q x + c q }$

Accepted Answer

A)  $\frac { k - y } { q - y }$ 
B)  x + c 
C)  $\frac { k } { q }$ 
D)  $\frac { k + y } { q + y }$ 
A)  $\frac { k - y } { q - y }$ 
B)  x + c 
C)  $\frac { k } { q }$ 
D)  $\frac { k + y } { q + y }$

Add the rational expressions. $\frac { 2 x } { x - 7 } + \frac { 16 } { x - 7 }$

Perform the indicated operations involving rational expressions. Match each expression with the corresponding answer. - $- \frac { x ^ { 3 } } { 56 y ^ { 2 } }$

Solve each equation. Match each equation with the corresponding solution. - $n = 0.75$

One angle of a triangle has a measure of $75 ^ { \circ }$ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles.

Kent drives his Mazda 250 miles in the same time that Dave drives his Nissan 225 miles. If Kent averages 5 miles per hour faster than Dave, find their rates.

Solve the equation. $n - \frac { 2 } { n } = \frac { 7 } { 2 }$

If two inlet pipes are both open, they can fill a pool in 2 hours and 24 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? __________ hours

Perform the indicated operation. $\frac { 27 } { x ^ { 2 } - 4 x - 21 } - \frac { 4 } { x ^ { 2 } - 6 x - 7 }$

Solve the equation. $5 + \frac { 25 } { n - 5 } = \frac { 125 } { n ^ { 2 } - 5 n }$

Solve the equation. $\frac { x } { 4 x ^ { 2 } + 6 x } - \frac { x } { 4 x ^ { 2 } + 10 x + 6 } = \frac { 3 } { x ^ { 2 } + x }$

An inlet pipe can fill a tank in 15 minutes. A drain can empty the tank in 20 minutes. If the tank is empty and both the pipe and drain are open, how long will it take before the tank overflows? __________ minutes

Solve the equation. $\frac { a } { a + 1 } - 7 = \frac { 8 a } { a + 1 }$

Solve the equation. $\frac { 5 } { n } + \frac { 1 } { 4 } = \frac { 13 } { 2 n }$

Perform the indicated operations involving rational expressions. Express the final answer in simplest form. $\frac { 6 n ^ { 2 } + 30 n - 36 } { 3 n ^ { 2 } + 10 n - 48 } \cdot \frac { 6 n ^ { 2 } - n - 40 } { 10 n ^ { 2 } + 15 n - 25 }$

Simplify the rational expression. $\frac { 28 x ^ { 3 } z } { - 30 x y z ^ { 2 } }$

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

To simplify a rational expression, divide out any common terms.

The ratio of male students to female students at a certain university is 3 to 2. If there is a total of 5,000 students, find the number of male students and the number of female students.

One angle of a triangle has a measure of $65 ^ { \circ }$ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles. and

Simplify the rational expression. $\frac { x y + c y + k x + c k } { x y + c y + q x + c q }$

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

Add the rational expressions. 2xx−7+16x−7\frac { 2 x } { x - 7 } + \frac { 16 } { x - 7 }x−72x​+x−716​

Perform the indicated operations involving rational expressions. Match each expression with the corresponding answer. - −x356y2- \frac { x ^ { 3 } } { 56 y ^ { 2 } }−56y2x3​

Solve each equation. Match each equation with the corresponding solution. - n=0.75n = 0.75n=0.75

One angle of a triangle has a measure of 75∘75 ^ { \circ }75∘ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles.

Kent drives his Mazda 250 miles in the same time that Dave drives his Nissan 225 miles. If Kent averages 5 miles per hour faster than Dave, find their rates.

Solve the equation. n−2n=72n - \frac { 2 } { n } = \frac { 7 } { 2 }n−n2​=27​

If two inlet pipes are both open, they can fill a pool in 2 hours and 24 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? __________ hours

Perform the indicated operation. 27x2−4x−21−4x2−6x−7\frac { 27 } { x ^ { 2 } - 4 x - 21 } - \frac { 4 } { x ^ { 2 } - 6 x - 7 }x2−4x−2127​−x2−6x−74​

Solve the equation. 5+25n−5=125n2−5n5 + \frac { 25 } { n - 5 } = \frac { 125 } { n ^ { 2 } - 5 n }5+n−525​=n2−5n125​

Solve the equation. x4x2+6x−x4x2+10x+6=3x2+x\frac { x } { 4 x ^ { 2 } + 6 x } - \frac { x } { 4 x ^ { 2 } + 10 x + 6 } = \frac { 3 } { x ^ { 2 } + x }4x2+6xx​−4x2+10x+6x​=x2+x3​

An inlet pipe can fill a tank in 15 minutes. A drain can empty the tank in 20 minutes. If the tank is empty and both the pipe and drain are open, how long will it take before the tank overflows? __________ minutes

Solve the equation. aa+1−7=8aa+1\frac { a } { a + 1 } - 7 = \frac { 8 a } { a + 1 }a+1a​−7=a+18a​

Solve the equation. 5n+14=132n\frac { 5 } { n } + \frac { 1 } { 4 } = \frac { 13 } { 2 n }n5​+41​=2n13​

Simplify the rational expression. 28x3z−30xyz2\frac { 28 x ^ { 3 } z } { - 30 x y z ^ { 2 } }−30xyz228x3z​

Simplify the rational expression. 4y−4xyx2y−y\frac { 4 y - 4 x y } { x ^ { 2 } y - y }x2y−y4y−4xy​

To simplify a rational expression, divide out any common terms.

The ratio of male students to female students at a certain university is 3 to 2. If there is a total of 5,000 students, find the number of male students and the number of female students.

One angle of a triangle has a measure of 65∘65 ^ { \circ }65∘ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles. __________ and __________

Simplify the rational expression. xy+cy+kx+ckxy+cy+qx+cq\frac { x y + c y + k x + c k } { x y + c y + q x + c q }xy+cy+qx+cqxy+cy+kx+ck​

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

Add the rational expressions. $\frac { 2 x } { x - 7 } + \frac { 16 } { x - 7 }$

Perform the indicated operations involving rational expressions. Match each expression with the corresponding answer. - $- \frac { x ^ { 3 } } { 56 y ^ { 2 } }$

Solve each equation. Match each equation with the corresponding solution. - $n = 0.75$

One angle of a triangle has a measure of $75 ^ { \circ }$ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles.

Solve the equation. $n - \frac { 2 } { n } = \frac { 7 } { 2 }$

Perform the indicated operation. $\frac { 27 } { x ^ { 2 } - 4 x - 21 } - \frac { 4 } { x ^ { 2 } - 6 x - 7 }$

Solve the equation. $5 + \frac { 25 } { n - 5 } = \frac { 125 } { n ^ { 2 } - 5 n }$

Solve the equation. $\frac { x } { 4 x ^ { 2 } + 6 x } - \frac { x } { 4 x ^ { 2 } + 10 x + 6 } = \frac { 3 } { x ^ { 2 } + x }$

Solve the equation. $\frac { a } { a + 1 } - 7 = \frac { 8 a } { a + 1 }$

Solve the equation. $\frac { 5 } { n } + \frac { 1 } { 4 } = \frac { 13 } { 2 n }$

Simplify the rational expression. $\frac { 28 x ^ { 3 } z } { - 30 x y z ^ { 2 } }$

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

One angle of a triangle has a measure of $65 ^ { \circ }$ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles. and

Simplify the rational expression. $\frac { x y + c y + k x + c k } { x y + c y + q x + c q }$