Question 1

Barry can do a certain job in 3 hours, whereas it takes Sanchez 4 hours to do the same job. How long would it take them to do the job working together? __________ hours

Accepted Answer

The answer of Barry can do a certain job in...

Question 2

Perform the indicated operation involving rational expressions. $\frac { 2 a ^ { 5 } b ^ { 5 } } { 3 a ^ { 4 } b ^ { 4 } } \cdot \frac { 9 a ^ { 6 } } { 8 a ^ { 4 } b ^ { 5 } }$

Accepted Answer

A)  $\frac { 3 a ^ { 2 } } { 4 b ^ { 5 } }$ 
B)  $\frac { 3 a ^ { 3 } } { 4 b ^ { 4 } }$ 
C)  $\frac { 4 a ^ { 3 } } { 3 b ^ { 4 } }$ 
D)  $\frac { 3 a ^ { 3 } } { b ^ { 5 } }$ 
A)  $\frac { 3 a ^ { 2 } } { 4 b ^ { 5 } }$ 
B)  $\frac { 3 a ^ { 3 } } { 4 b ^ { 4 } }$ 
C)  $\frac { 4 a ^ { 3 } } { 3 b ^ { 4 } }$ 
D)  $\frac { 3 a ^ { 3 } } { b ^ { 5 } }$

Question 3

Perform the indicated operation involving rational expressions. $\frac { 3 a ^ { 2 } - 18 a } { a ^ { 3 } - 7 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 14 a + 49 } { a ^ { 2 } - 36 }$

Accepted Answer

A)  $\frac { 3 a - 21 } { a ^ { 2 } + 6 a }$ 
B)  $\frac { 21 } { a ^ { 2 } + 3 a }$ 
C)  $\frac { 3 a ^ { 2 } + 21 } { a ^ { 2 } + 6 a }$ 
D)  $\frac { 3 } { a ^ { 2 } + 6 a }$ 
E)  $\frac { a - 7 } { a ^ { 2 } + 6 a }$ 
A)  $\frac { 3 a - 21 } { a ^ { 2 } + 6 a }$ 
B)  $\frac { 21 } { a ^ { 2 } + 3 a }$ 
C)  $\frac { 3 a ^ { 2 } + 21 } { a ^ { 2 } + 6 a }$ 
D)  $\frac { 3 } { a ^ { 2 } + 6 a }$ 
E)  $\frac { a - 7 } { a ^ { 2 } + 6 a }$

Question 4

Add or subtract the rational expressions. $\frac { 3 } { 2 x } + \frac { 4 } { 3 y } - 3$

Accepted Answer

The answer of Add or subtract the rational expressions. \(\frac...

Question 5

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 15 } { 7 x ^ { 2 } } - \frac { 21 } { 10 x } - \frac { 11 } { 5 x }$

Accepted Answer

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

Question 6

The quotient of two rational expressions is the product obtained when multiplying the first expression by the reciprocal of the second.

Accepted Answer

A) True 
 B)False

Question 7

The sum of two numbers is 48. If the larger is divided by the smaller, the quotient is 10 and the remainder is 4. Find the numbers.

Accepted Answer

A)  45 and 3 
B)  42 and 6 
C)  39 and 9 
D)  44 and 4 
E)  41 and 7 
A)  45 and 3 
B)  42 and 6 
C)  39 and 9 
D)  44 and 4 
E)  41 and 7

Question 8

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 8 x ^ { 9 } y ^ { 9 } } { 9 x ^ { 10 } y ^ { 8 } } \cdot \frac { 63 x ^ { 9 } } { 64 y } \cdot \frac { 8 x } { y ^ { 8 } }$

Accepted Answer

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

Question 9

Solve the equation. $\frac { 9 x - 35 } { 5 } = \frac { 10 } { x }$

Accepted Answer

A)  $\left\{ \frac { 10 } { 9 } , - 5 \right\}$ 
B)  $\left\{ - \frac { 19 } { 9 } , - 5 \right\}$ 
C)  $\left\{ - \frac { 10 } { 9 } , 5 \right\}$ 
D)  $\left\{ \frac { 19 } { 9 } , 5 \right\}$ 
A)  $\left\{ \frac { 10 } { 9 } , - 5 \right\}$ 
B)  $\left\{ - \frac { 19 } { 9 } , - 5 \right\}$ 
C)  $\left\{ - \frac { 10 } { 9 } , 5 \right\}$ 
D)  $\left\{ \frac { 19 } { 9 } , 5 \right\}$

Question 10

Simplify the rational expression. $\frac { 5 y ^ { 2 } + 39 y + 28 } { 25 y ^ { 2 } - 16 }$

Accepted Answer

A)  $\frac { y } { y - 4 }$ 
B)  $\frac { y + 7 } { 5 y - 4 }$ 
C)  $\frac { y - 7 } { y + 4 }$ 
D)  $\frac { y + 7 } { 5 y - 16 }$ 
A)  $\frac { y } { y - 4 }$ 
B)  $\frac { y + 7 } { 5 y - 4 }$ 
C)  $\frac { y - 7 } { y + 4 }$ 
D)  $\frac { y + 7 } { 5 y - 16 }$

Question 11

Solve the equation. $\frac { x } { 7 x - 7 } + \frac { 4 } { x ^ { 2 } - 1 } = \frac { 1 } { 7 }$

Accepted Answer

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

Question 12

A sum of $1,740 is to be divided between two people in the ratio of 2 to 4. How much does each person receive? $__________ and $__________

Accepted Answer

The answer of A sum of $1,740 is to be...

Question 13

Simplify the rational expression. $\frac { 44 x ^ { 3 } z } { - 48 x y z ^ { 2 } }$

Accepted Answer

A)  $\frac { 11 x ^ { 2 } } { 12 z }$ 
B)  $- \frac { 44 x } { 48 y z }$ 
C)  $- \frac { 11 x ^ { 2 } } { 12 y z }$ 
D)  $\frac { x ^ { 2 } } { 4 y z }$ 
A)  $\frac { 11 x ^ { 2 } } { 12 z }$ 
B)  $- \frac { 44 x } { 48 y z }$ 
C)  $- \frac { 11 x ^ { 2 } } { 12 y z }$ 
D)  $\frac { x ^ { 2 } } { 4 y z }$

Question 14

The least common denominator of $\frac { \frac { 4 } { 5 } + \frac { 3 } { 15 } } { \frac { 2 } { 3 } - \frac { 3 } { 5 } }$ is 15.

Accepted Answer

A) True 
 B)False

Question 15

Perform the indicated operation involving rational expressions. $\frac { 5 x ^ { 8 } y ^ { 8 } } { 6 x ^ { 9 } y ^ { 7 } } \cdot \frac { 18 x ^ { 8 } } { 20 }$

Accepted Answer

A)  $\frac { 3 x y ^ { 9 } } { 4 }$ 
B)  $\frac { 4 x y ^ { 7 } } { 3 }$ 
C)  $\frac { 3 x y ^ { 7 } } { 4 }$ 
D)  $\frac { 4 x y ^ { 8 } } { 3 }$ 
A)  $\frac { 3 x y ^ { 9 } } { 4 }$ 
B)  $\frac { 4 x y ^ { 7 } } { 3 }$ 
C)  $\frac { 3 x y ^ { 7 } } { 4 }$ 
D)  $\frac { 4 x y ^ { 8 } } { 3 }$

Question 16

Simplify the complex fraction. $\frac { \frac { 5 } { 12 x } } { \frac { 20 } { 3 x y } }$

Accepted Answer

A)  $\frac { x y } { 16 }$ 
B)  $\frac { x } { 4 y }$ 
C)  $\frac { y } { 4 }$ 
D)  $\frac { y } { 16 }$ 
A)  $\frac { x y } { 16 }$ 
B)  $\frac { x } { 4 y }$ 
C)  $\frac { y } { 4 }$ 
D)  $\frac { y } { 16 }$

Question 17

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 1 } { 4 } + \frac { 7 } { 8 } - \frac { 7 } { 16 }$

Accepted Answer

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

Question 18

Barry can do a certain job in 2 hours, whereas it takes Sanchez 3 hours to do the same job. How long would it take them to do the job working together?

Accepted Answer

A)  $1 \frac { 5 } { 6 } \text { hours }$ 
B)  $1 \frac { 1 } { 5 } \text { hours }$ 
C)  $\frac { 5 } { 6 } \text { hours }$ 
A)  $1 \frac { 5 } { 6 } \text { hours }$ 
B)  $1 \frac { 1 } { 5 } \text { hours }$ 
C)  $\frac { 5 } { 6 } \text { hours }$

Question 19

Perform the indicated operation involving rational expressions. $\frac { 8 a ^ { 2 } - 64 a } { a ^ { 3 } - 8 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 16 a + 64 } { a ^ { 2 } - 64 }$

Accepted Answer

A)  $\frac { 8 a ^ { 2 } + 64 } { a ^ { 2 } + 8 a }$ 
B)  $\frac { a - 8 } { a ^ { 2 } + 8 a }$ 
C)  $\frac { 8 } { a ^ { 2 } + 8 a }$ 
D)  $\frac { 8 a - 64 } { a ^ { 2 } + 8 a }$ 
A)  $\frac { 8 a ^ { 2 } + 64 } { a ^ { 2 } + 8 a }$ 
B)  $\frac { a - 8 } { a ^ { 2 } + 8 a }$ 
C)  $\frac { 8 } { a ^ { 2 } + 8 a }$ 
D)  $\frac { 8 a - 64 } { a ^ { 2 } + 8 a }$

Question 20

Consider the addition problem. $$\frac { 8 } { x - 2 } + \frac { 5 } { 2 - x }$$ Note that the denominators are opposites of each other. If the property $$\frac { a } { - b } = - \frac { a } { b }$$ is applied to the second fraction, we have $$\frac { 5 } { 2 - x } = - \frac { 5 } { x - 2 }$$ Thus we proceed as follows: $$\frac { 8 } { x - 2 } + \frac { 5 } { 2 - x } = \frac { 8 } { x - 2 } - \frac { 5 } { x - 2 } = \frac { 8 - 5 } { x - 2 } = \frac { 3 } { x - 2 }$$ Use this approach to do the following problem. $$\frac { 9 } { a - 2 } - \frac { 1 } { 2 - a }$$

Accepted Answer

The answer of Consider the addition problem. \[\frac { 8...

Barry can do a certain job in 3 hours, whereas it takes Sanchez 4 hours to do the same job. How long would it take them to do the job working together? __________ hours

Perform the indicated operation involving rational expressions. $\frac { 2 a ^ { 5 } b ^ { 5 } } { 3 a ^ { 4 } b ^ { 4 } } \cdot \frac { 9 a ^ { 6 } } { 8 a ^ { 4 } b ^ { 5 } }$

Perform the indicated operation involving rational expressions. $\frac { 3 a ^ { 2 } - 18 a } { a ^ { 3 } - 7 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 14 a + 49 } { a ^ { 2 } - 36 }$

Add or subtract the rational expressions. $\frac { 3 } { 2 x } + \frac { 4 } { 3 y } - 3$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 15 } { 7 x ^ { 2 } } - \frac { 21 } { 10 x } - \frac { 11 } { 5 x }$

The quotient of two rational expressions is the product obtained when multiplying the first expression by the reciprocal of the second.

The sum of two numbers is 48. If the larger is divided by the smaller, the quotient is 10 and the remainder is 4. Find the numbers.

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 8 x ^ { 9 } y ^ { 9 } } { 9 x ^ { 10 } y ^ { 8 } } \cdot \frac { 63 x ^ { 9 } } { 64 y } \cdot \frac { 8 x } { y ^ { 8 } }$

Solve the equation. $\frac { 9 x - 35 } { 5 } = \frac { 10 } { x }$

Simplify the rational expression. $\frac { 5 y ^ { 2 } + 39 y + 28 } { 25 y ^ { 2 } - 16 }$

Solve the equation. $\frac { x } { 7 x - 7 } + \frac { 4 } { x ^ { 2 } - 1 } = \frac { 1 } { 7 }$

A sum of $1,740 is to be divided between two people in the ratio of 2 to 4. How much does each person receive? $ and $

Simplify the rational expression. $\frac { 44 x ^ { 3 } z } { - 48 x y z ^ { 2 } }$

The least common denominator of $\frac { \frac { 4 } { 5 } + \frac { 3 } { 15 } } { \frac { 2 } { 3 } - \frac { 3 } { 5 } }$ is 15.

Perform the indicated operation involving rational expressions. $\frac { 5 x ^ { 8 } y ^ { 8 } } { 6 x ^ { 9 } y ^ { 7 } } \cdot \frac { 18 x ^ { 8 } } { 20 }$

Simplify the complex fraction. $\frac { \frac { 5 } { 12 x } } { \frac { 20 } { 3 x y } }$

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 1 } { 4 } + \frac { 7 } { 8 } - \frac { 7 } { 16 }$

Barry can do a certain job in 2 hours, whereas it takes Sanchez 3 hours to do the same job. How long would it take them to do the job working together?

Perform the indicated operation involving rational expressions. $\frac { 8 a ^ { 2 } - 64 a } { a ^ { 3 } - 8 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 16 a + 64 } { a ^ { 2 } - 64 }$

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

Barry can do a certain job in 3 hours, whereas it takes Sanchez 4 hours to do the same job. How long would it take them to do the job working together? __________ hours

Perform the indicated operation involving rational expressions. 2a5b53a4b4⋅9a68a4b5\frac { 2 a ^ { 5 } b ^ { 5 } } { 3 a ^ { 4 } b ^ { 4 } } \cdot \frac { 9 a ^ { 6 } } { 8 a ^ { 4 } b ^ { 5 } }3a4b42a5b5​⋅8a4b59a6​

Perform the indicated operation involving rational expressions. 3a2−18aa3−7a2⋅a2−14a+49a2−36\frac { 3 a ^ { 2 } - 18 a } { a ^ { 3 } - 7 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 14 a + 49 } { a ^ { 2 } - 36 }a3−7a23a2−18a​⋅a2−36a2−14a+49​

Add or subtract the rational expressions. 32x+43y−3\frac { 3 } { 2 x } + \frac { 4 } { 3 y } - 32x3​+3y4​−3

Subtract the rational expressions. Be sure to express your answer in simplest form. 157x2−2110x−115x\frac { 15 } { 7 x ^ { 2 } } - \frac { 21 } { 10 x } - \frac { 11 } { 5 x }7x215​−10x21​−5x11​

The quotient of two rational expressions is the product obtained when multiplying the first expression by the reciprocal of the second.

The sum of two numbers is 48. If the larger is divided by the smaller, the quotient is 10 and the remainder is 4. Find the numbers.

Perform the indicated operation involving rational expressions. Express final answer in simplest form. 8x9y99x10y8⋅63x964y⋅8xy8\frac { 8 x ^ { 9 } y ^ { 9 } } { 9 x ^ { 10 } y ^ { 8 } } \cdot \frac { 63 x ^ { 9 } } { 64 y } \cdot \frac { 8 x } { y ^ { 8 } }9x10y88x9y9​⋅64y63x9​⋅y88x​

Solve the equation. 9x−355=10x\frac { 9 x - 35 } { 5 } = \frac { 10 } { x }59x−35​=x10​

Simplify the rational expression. 5y2+39y+2825y2−16\frac { 5 y ^ { 2 } + 39 y + 28 } { 25 y ^ { 2 } - 16 }25y2−165y2+39y+28​

Solve the equation. x7x−7+4x2−1=17\frac { x } { 7 x - 7 } + \frac { 4 } { x ^ { 2 } - 1 } = \frac { 1 } { 7 }7x−7x​+x2−14​=71​

A sum of $1,740 is to be divided between two people in the ratio of 2 to 4. How much does each person receive? $__________ and $__________

Simplify the rational expression. 44x3z−48xyz2\frac { 44 x ^ { 3 } z } { - 48 x y z ^ { 2 } }−48xyz244x3z​

The least common denominator of 45+31523−35\frac { \frac { 4 } { 5 } + \frac { 3 } { 15 } } { \frac { 2 } { 3 } - \frac { 3 } { 5 } }32​−53​54​+153​​ is 15.

Perform the indicated operation involving rational expressions. 5x8y86x9y7⋅18x820\frac { 5 x ^ { 8 } y ^ { 8 } } { 6 x ^ { 9 } y ^ { 7 } } \cdot \frac { 18 x ^ { 8 } } { 20 }6x9y75x8y8​⋅2018x8​

Simplify the complex fraction. 512x203xy\frac { \frac { 5 } { 12 x } } { \frac { 20 } { 3 x y } }3xy20​12x5​​

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. 14+78−716\frac { 1 } { 4 } + \frac { 7 } { 8 } - \frac { 7 } { 16 }41​+87​−167​

Barry can do a certain job in 2 hours, whereas it takes Sanchez 3 hours to do the same job. How long would it take them to do the job working together?

Perform the indicated operation involving rational expressions. 8a2−64aa3−8a2⋅a2−16a+64a2−64\frac { 8 a ^ { 2 } - 64 a } { a ^ { 3 } - 8 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 16 a + 64 } { a ^ { 2 } - 64 }a3−8a28a2−64a​⋅a2−64a2−16a+64​

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

Perform the indicated operation involving rational expressions. $\frac { 2 a ^ { 5 } b ^ { 5 } } { 3 a ^ { 4 } b ^ { 4 } } \cdot \frac { 9 a ^ { 6 } } { 8 a ^ { 4 } b ^ { 5 } }$

Perform the indicated operation involving rational expressions. $\frac { 3 a ^ { 2 } - 18 a } { a ^ { 3 } - 7 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 14 a + 49 } { a ^ { 2 } - 36 }$

Add or subtract the rational expressions. $\frac { 3 } { 2 x } + \frac { 4 } { 3 y } - 3$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 15 } { 7 x ^ { 2 } } - \frac { 21 } { 10 x } - \frac { 11 } { 5 x }$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 8 x ^ { 9 } y ^ { 9 } } { 9 x ^ { 10 } y ^ { 8 } } \cdot \frac { 63 x ^ { 9 } } { 64 y } \cdot \frac { 8 x } { y ^ { 8 } }$

Solve the equation. $\frac { 9 x - 35 } { 5 } = \frac { 10 } { x }$

Simplify the rational expression. $\frac { 5 y ^ { 2 } + 39 y + 28 } { 25 y ^ { 2 } - 16 }$

Solve the equation. $\frac { x } { 7 x - 7 } + \frac { 4 } { x ^ { 2 } - 1 } = \frac { 1 } { 7 }$

A sum of $1,740 is to be divided between two people in the ratio of 2 to 4. How much does each person receive? $ and $

Simplify the rational expression. $\frac { 44 x ^ { 3 } z } { - 48 x y z ^ { 2 } }$

The least common denominator of $\frac { \frac { 4 } { 5 } + \frac { 3 } { 15 } } { \frac { 2 } { 3 } - \frac { 3 } { 5 } }$ is 15.

Perform the indicated operation involving rational expressions. $\frac { 5 x ^ { 8 } y ^ { 8 } } { 6 x ^ { 9 } y ^ { 7 } } \cdot \frac { 18 x ^ { 8 } } { 20 }$

Simplify the complex fraction. $\frac { \frac { 5 } { 12 x } } { \frac { 20 } { 3 x y } }$

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 1 } { 4 } + \frac { 7 } { 8 } - \frac { 7 } { 16 }$

Perform the indicated operation involving rational expressions. $\frac { 8 a ^ { 2 } - 64 a } { a ^ { 3 } - 8 a ^ { 2 } } \cdot \frac { a ^ { 2 } - 16 a + 64 } { a ^ { 2 } - 64 }$