Exam 9: Rational Expressions

Perform the indicated operation and express your answer in simplest form. $\frac { 1 } { x ^ { 2 } - 3 x - 4 } - \frac { 2 } { x - 4 } - \frac { 5 } { x + 1 }$ Please enter your answer as one fraction with the denominator factored completely.

(Short Answer)

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Question 21

Solve the equation for the variable x . $y = - \frac { v } { g } x + \frac { e } { m }$

(Short Answer)

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Question 22

Perform the indicated operation involving rational numbers. $\frac { - 6 } { 7 } \cdot \frac { 35 } { 78 }$

(Multiple Choice)

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Question 23

Simplify the complex fraction. $\frac { \frac { 5 } { x } - \frac { 6 } { y } } { \frac { 7 } { y } - \frac { 2 } { x y } }$

(Short Answer)

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Question 24

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

(Multiple Choice)

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Question 25

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 8 } { 3 n } - \frac { 6 } { 2 n ^ { 2 } }$

(Short Answer)

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Question 26

Simplify the rational expression. $\frac { a ^ { 2 } - 25 } { 5 - a }$

(Multiple Choice)

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Question 27

Perform the indicated operation involving rational expressions. $\frac { 2 x + 14 } { 11 y } \div \frac { x ^ { 2 } + 14 x + 49 } { x ^ { 2 } + 2 }$

(Multiple Choice)

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Question 28

Perform the indicated operation involving rational expressions. $\frac { 2 x + 4 } { 11 y } \cdot \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 4 x + 4 }$

(Multiple Choice)

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Question 29

Solve the equation. $\frac { x + 4 } { 5 } - \frac { x - 2 } { 6 } = 1$

(Short Answer)

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Question 30

Solve the equation. $\frac { 15 - n } { n } = 7 + \frac { 7 } { n }$

(Short Answer)

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Question 31

Solve the equation. $\frac { n } { 5 } = \frac { 6 } { n - 1 }$

(Short Answer)

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Question 32

Express the rational number in reduced form. $\frac { 30 } { - 36 }$

(Short Answer)

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Question 33

Solve each equation for the variable Q . $I = \frac { 300 Q } { D }$

(Multiple Choice)

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Question 34

Solve the equation. $\frac { 51 - n } { n } = 5 + \frac { 3 } { n }$

(Multiple Choice)

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Question 35

Solve each equation for the variable y . $\frac { y - b } { x } = m$

(Multiple Choice)

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Question 36

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 9 a ^ { 5 } b ^ { 5 } } { 10 a ^ { 4 } c b ^ { 4 } } \div \frac { 72 c a ^ { 4 } b ^ { 5 } } { 70 a ^ { 6 } }$

(Short Answer)

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Question 37

Perform the indicated operations involving rational numbers. Express final answer in reduced form. $\frac { - 16 } { 8 } \div \frac { 64 } { 24 }$

(Multiple Choice)

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Question 38

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

(Short Answer)

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Question 39

Solve the equation. $\frac { x } { x + 3 } + 3 = \frac { 11 } { x + 3 }$

(Short Answer)

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Question 40

Perform the indicated operation and express your answer in simplest form. $\frac { 1 } { x ^ { 2 } - 3 x - 4 } - \frac { 2 } { x - 4 } - \frac { 5 } { x + 1 }$ Please enter your answer as one fraction with the denominator factored completely.

Solve the equation for the variable x . $y = - \frac { v } { g } x + \frac { e } { m }$

Perform the indicated operation involving rational numbers. $\frac { - 6 } { 7 } \cdot \frac { 35 } { 78 }$

Simplify the complex fraction. $\frac { \frac { 5 } { x } - \frac { 6 } { y } } { \frac { 7 } { y } - \frac { 2 } { x y } }$

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

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 8 } { 3 n } - \frac { 6 } { 2 n ^ { 2 } }$

Simplify the rational expression. $\frac { a ^ { 2 } - 25 } { 5 - a }$

Perform the indicated operation involving rational expressions. $\frac { 2 x + 14 } { 11 y } \div \frac { x ^ { 2 } + 14 x + 49 } { x ^ { 2 } + 2 }$

Perform the indicated operation involving rational expressions. $\frac { 2 x + 4 } { 11 y } \cdot \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 4 x + 4 }$

Solve the equation. $\frac { x + 4 } { 5 } - \frac { x - 2 } { 6 } = 1$

Solve the equation. $\frac { 15 - n } { n } = 7 + \frac { 7 } { n }$

Solve the equation. $\frac { n } { 5 } = \frac { 6 } { n - 1 }$

Express the rational number in reduced form. $\frac { 30 } { - 36 }$

Solve each equation for the variable Q . $I = \frac { 300 Q } { D }$

Solve the equation. $\frac { 51 - n } { n } = 5 + \frac { 3 } { n }$

Solve each equation for the variable y . $\frac { y - b } { x } = m$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 9 a ^ { 5 } b ^ { 5 } } { 10 a ^ { 4 } c b ^ { 4 } } \div \frac { 72 c a ^ { 4 } b ^ { 5 } } { 70 a ^ { 6 } }$

Perform the indicated operations involving rational numbers. Express final answer in reduced form. $\frac { - 16 } { 8 } \div \frac { 64 } { 24 }$

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

Solve the equation. $\frac { x } { x + 3 } + 3 = \frac { 11 } { x + 3 }$

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 for the variable x . y=−vgx+emy = - \frac { v } { g } x + \frac { e } { m }y=−gv​x+me​

Perform the indicated operation involving rational numbers. −67⋅3578\frac { - 6 } { 7 } \cdot \frac { 35 } { 78 }7−6​⋅7835​

Simplify the complex fraction. 5x−6y7y−2xy\frac { \frac { 5 } { x } - \frac { 6 } { y } } { \frac { 7 } { y } - \frac { 2 } { x y } }y7​−xy2​x5​−y6​​

Add the rational expressions.Be sure to express your answer in simplest form. 52x+3+25x+3\frac { 5 } { 2 x + 3 } + \frac { 2 } { 5 x + 3 }2x+35​+5x+32​

Subtract the rational expressions. Be sure to express your answer in simplest form. 83n−62n2\frac { 8 } { 3 n } - \frac { 6 } { 2 n ^ { 2 } }3n8​−2n26​

Simplify the rational expression. a2−255−a\frac { a ^ { 2 } - 25 } { 5 - a }5−aa2−25​

Perform the indicated operation involving rational expressions. 2x+1411y÷x2+14x+49x2+2\frac { 2 x + 14 } { 11 y } \div \frac { x ^ { 2 } + 14 x + 49 } { x ^ { 2 } + 2 }11y2x+14​÷x2+2x2+14x+49​

Perform the indicated operation involving rational expressions. 2x+411y⋅x2+5x2+4x+4\frac { 2 x + 4 } { 11 y } \cdot \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 4 x + 4 }11y2x+4​⋅x2+4x+4x2+5​

Solve the equation. x+45−x−26=1\frac { x + 4 } { 5 } - \frac { x - 2 } { 6 } = 15x+4​−6x−2​=1

Solve the equation. 15−nn=7+7n\frac { 15 - n } { n } = 7 + \frac { 7 } { n }n15−n​=7+n7​

Solve the equation. n5=6n−1\frac { n } { 5 } = \frac { 6 } { n - 1 }5n​=n−16​

Express the rational number in reduced form. 30−36\frac { 30 } { - 36 }−3630​

Solve each equation for the variable Q . I=300QDI = \frac { 300 Q } { D }I=D300Q​

Solve the equation. 51−nn=5+3n\frac { 51 - n } { n } = 5 + \frac { 3 } { n }n51−n​=5+n3​

Solve each equation for the variable y . y−bx=m\frac { y - b } { x } = mxy−b​=m

Perform the indicated operation involving rational expressions. Express final answer in simplest form. 9a5b510a4cb4÷72ca4b570a6\frac { 9 a ^ { 5 } b ^ { 5 } } { 10 a ^ { 4 } c b ^ { 4 } } \div \frac { 72 c a ^ { 4 } b ^ { 5 } } { 70 a ^ { 6 } }10a4cb49a5b5​÷70a672ca4b5​

Perform the indicated operations involving rational numbers. Express final answer in reduced form. −168÷6424\frac { - 16 } { 8 } \div \frac { 64 } { 24 }8−16​÷2464​

Solve the equation. xx+3+3=11x+3\frac { x } { x + 3 } + 3 = \frac { 11 } { x + 3 }x+3x​+3=x+311​

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 for the variable x . $y = - \frac { v } { g } x + \frac { e } { m }$

Perform the indicated operation involving rational numbers. $\frac { - 6 } { 7 } \cdot \frac { 35 } { 78 }$

Simplify the complex fraction. $\frac { \frac { 5 } { x } - \frac { 6 } { y } } { \frac { 7 } { y } - \frac { 2 } { x y } }$

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

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 8 } { 3 n } - \frac { 6 } { 2 n ^ { 2 } }$

Simplify the rational expression. $\frac { a ^ { 2 } - 25 } { 5 - a }$

Perform the indicated operation involving rational expressions. $\frac { 2 x + 14 } { 11 y } \div \frac { x ^ { 2 } + 14 x + 49 } { x ^ { 2 } + 2 }$

Perform the indicated operation involving rational expressions. $\frac { 2 x + 4 } { 11 y } \cdot \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 4 x + 4 }$

Solve the equation. $\frac { x + 4 } { 5 } - \frac { x - 2 } { 6 } = 1$

Solve the equation. $\frac { 15 - n } { n } = 7 + \frac { 7 } { n }$

Solve the equation. $\frac { n } { 5 } = \frac { 6 } { n - 1 }$

Express the rational number in reduced form. $\frac { 30 } { - 36 }$

Solve each equation for the variable Q . $I = \frac { 300 Q } { D }$

Solve the equation. $\frac { 51 - n } { n } = 5 + \frac { 3 } { n }$

Solve each equation for the variable y . $\frac { y - b } { x } = m$

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 9 a ^ { 5 } b ^ { 5 } } { 10 a ^ { 4 } c b ^ { 4 } } \div \frac { 72 c a ^ { 4 } b ^ { 5 } } { 70 a ^ { 6 } }$

Perform the indicated operations involving rational numbers. Express final answer in reduced form. $\frac { - 16 } { 8 } \div \frac { 64 } { 24 }$

Solve the equation. $\frac { x } { x + 3 } + 3 = \frac { 11 } { x + 3 }$