Exam 9: Rational Expressions

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

(Short Answer)

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Question 41

Perform the indicated operation involving rational numbers. $\frac { 2 } { - 3 } \cdot \frac { - 15 } { 16 }$

(Multiple Choice)

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Question 42

The numbers $\frac { - 3 } { 7 }$ and $\frac { - 7 } { 3 }$ are multiplicative inverses.

(True/False)

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Question 43

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { a - 7 } { a } - \frac { 1 } { a + 7 }$ Please enter your answer as one fraction with the denominator factored completely and the numerator not factored.

(Short Answer)

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Question 44

Perform the indicated operation and express your answer in simplest form. $\frac { 7 n } { n ^ { 2 } - 25 } - \frac { 5 } { 2 n - 10 }$ Please enter your answer as one fraction with the denominator factored completely.

(Short Answer)

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Question 45

Solve the equation for the variable x . $y = \frac { 5 } { 6 } x + \frac { 3 } { 12 }$

(Short Answer)

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Question 46

Perform the indicated operations involving rational expressions. Match each expression with the corresponding answer. - $- \frac { 7 x ^ { 3 } y ^ { 3 } } { 8 }$

(Multiple Choice)

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Question 47

Perform the operation involving rational numbers. $\frac { 1 } { 4 } + \frac { 7 } { 8 } - \frac { 7 } { 16 }$

(Multiple Choice)

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Question 48

Express the rational number in reduced form. $\frac { 45 } { 54 }$

(Short Answer)

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Question 49

Simplify the rational expression. $\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 3 x }$

(Short Answer)

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Question 50

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { x - 3 } { 9 } + \frac { x + 9 } { 10 }$

(Multiple Choice)

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Question 51

Express the rational number in reduced form. $\frac { 65 } { - 78 }$

(Multiple Choice)

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Question 52

The least common denominator of $\frac { 7 } { x - 1 } + \frac { 3 } { 1 - x }$ is $x - 1$ .

(True/False)

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Question 53

Simplify the rational expression. $\frac { 64 x ^ { 4 } + 27 x } { 12 x ^ { 3 } - 63 x ^ { 2 } - 54 x }$

(Short Answer)

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Question 54

Perform the indicated operation involving rational numbers. Express final answer in reduced form. $\frac { - 3 } { 4 } \cdot \frac { 28 } { 39 }$

(Short Answer)

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Question 55

Solve the equation. $\frac { x } { x + 2 } + 3 = \frac { 7 } { x + 2 }$

(Multiple Choice)

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Question 56

Simplify the complex fraction. $\frac { - \frac { 5 } { x } - \frac { 10 } { x + 5 } } { \frac { 3 } { x ^ { 2 } + 5 x } + \frac { 3 } { x } }$

(Multiple Choice)

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Question 57

If the indicated quotient of rational expression is $- 1$ , then the numerator and denominator are opposites.

(True/False)

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Question 58

Simplify the rational expression. $\frac { x ^ { 4 } - 2 x ^ { 2 } - 48 } { 4 x ^ { 4 } + 29 x ^ { 2 } + 30 }$

(Multiple Choice)

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Question 59

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 4 x } - \frac { 6 } { x }$ Please enter your answer as one fraction with the denominator factored completely.

(Short Answer)

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Question 60

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

Perform the indicated operation involving rational numbers. $\frac { 2 } { - 3 } \cdot \frac { - 15 } { 16 }$

The numbers $\frac { - 3 } { 7 }$ and $\frac { - 7 } { 3 }$ are multiplicative inverses.

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { a - 7 } { a } - \frac { 1 } { a + 7 }$ Please enter your answer as one fraction with the denominator factored completely and the numerator not factored.

Perform the indicated operation and express your answer in simplest form. $\frac { 7 n } { n ^ { 2 } - 25 } - \frac { 5 } { 2 n - 10 }$ Please enter your answer as one fraction with the denominator factored completely.

Solve the equation for the variable x . $y = \frac { 5 } { 6 } x + \frac { 3 } { 12 }$

Perform the indicated operations involving rational expressions. Match each expression with the corresponding answer. - $- \frac { 7 x ^ { 3 } y ^ { 3 } } { 8 }$

Perform the operation involving rational numbers. $\frac { 1 } { 4 } + \frac { 7 } { 8 } - \frac { 7 } { 16 }$

Express the rational number in reduced form. $\frac { 45 } { 54 }$

Simplify the rational expression. $\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 3 x }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { x - 3 } { 9 } + \frac { x + 9 } { 10 }$

Express the rational number in reduced form. $\frac { 65 } { - 78 }$

The least common denominator of $\frac { 7 } { x - 1 } + \frac { 3 } { 1 - x }$ is $x - 1$ .

Simplify the rational expression. $\frac { 64 x ^ { 4 } + 27 x } { 12 x ^ { 3 } - 63 x ^ { 2 } - 54 x }$

Perform the indicated operation involving rational numbers. Express final answer in reduced form. $\frac { - 3 } { 4 } \cdot \frac { 28 } { 39 }$

Solve the equation. $\frac { x } { x + 2 } + 3 = \frac { 7 } { x + 2 }$

Simplify the complex fraction. $\frac { - \frac { 5 } { x } - \frac { 10 } { x + 5 } } { \frac { 3 } { x ^ { 2 } + 5 x } + \frac { 3 } { x } }$

If the indicated quotient of rational expression is $- 1$ , then the numerator and denominator are opposites.

Simplify the rational expression. $\frac { x ^ { 4 } - 2 x ^ { 2 } - 48 } { 4 x ^ { 4 } + 29 x ^ { 2 } + 30 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 4 x } - \frac { 6 } { x }$ Please enter your answer as one fraction with the denominator factored completely.

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

Perform the indicated operation and express your answer in simplest form. 3xx2+4x+4x\frac { 3 x } { x ^ { 2 } + 4 x } + \frac { 4 } { x }x2+4x3x​+x4​ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation involving rational numbers. 2−3⋅−1516\frac { 2 } { - 3 } \cdot \frac { - 15 } { 16 }−32​⋅16−15​

The numbers −37\frac { - 3 } { 7 }7−3​ and −73\frac { - 7 } { 3 }3−7​ are multiplicative inverses.

Add the rational expressions. Be sure to express your answer in simplest form. a−7a−1a+7\frac { a - 7 } { a } - \frac { 1 } { a + 7 }aa−7​−a+71​ Please enter your answer as one fraction with the denominator factored completely and the numerator not factored.

Perform the indicated operation and express your answer in simplest form. 7nn2−25−52n−10\frac { 7 n } { n ^ { 2 } - 25 } - \frac { 5 } { 2 n - 10 }n2−257n​−2n−105​ Please enter your answer as one fraction with the denominator factored completely.

Solve the equation for the variable x . y=56x+312y = \frac { 5 } { 6 } x + \frac { 3 } { 12 }y=65​x+123​

Perform the indicated operations involving rational expressions. Match each expression with the corresponding answer. - −7x3y38- \frac { 7 x ^ { 3 } y ^ { 3 } } { 8 }−87x3y3​

Perform the operation involving rational numbers. 14+78−716\frac { 1 } { 4 } + \frac { 7 } { 8 } - \frac { 7 } { 16 }41​+87​−167​

Express the rational number in reduced form. 4554\frac { 45 } { 54 }5445​

Simplify the rational expression. x2−9x2+3x\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 3 x }x2+3xx2−9​

Add the rational expressions. Be sure to express your answer in simplest form. x−39+x+910\frac { x - 3 } { 9 } + \frac { x + 9 } { 10 }9x−3​+10x+9​

Express the rational number in reduced form. 65−78\frac { 65 } { - 78 }−7865​

The least common denominator of 7x−1+31−x\frac { 7 } { x - 1 } + \frac { 3 } { 1 - x }x−17​+1−x3​ is x−1x - 1x−1 .

Simplify the rational expression. 64x4+27x12x3−63x2−54x\frac { 64 x ^ { 4 } + 27 x } { 12 x ^ { 3 } - 63 x ^ { 2 } - 54 x }12x3−63x2−54x64x4+27x​

Perform the indicated operation involving rational numbers. Express final answer in reduced form. −34⋅2839\frac { - 3 } { 4 } \cdot \frac { 28 } { 39 }4−3​⋅3928​

Solve the equation. xx+2+3=7x+2\frac { x } { x + 2 } + 3 = \frac { 7 } { x + 2 }x+2x​+3=x+27​

Simplify the complex fraction. −5x−10x+53x2+5x+3x\frac { - \frac { 5 } { x } - \frac { 10 } { x + 5 } } { \frac { 3 } { x ^ { 2 } + 5 x } + \frac { 3 } { x } }x2+5x3​+x3​−x5​−x+510​​

If the indicated quotient of rational expression is −1- 1−1 , then the numerator and denominator are opposites.

Simplify the rational expression. x4−2x2−484x4+29x2+30\frac { x ^ { 4 } - 2 x ^ { 2 } - 48 } { 4 x ^ { 4 } + 29 x ^ { 2 } + 30 }4x4+29x2+30x4−2x2−48​

Perform the indicated operation and express your answer in simplest form. 7xx2+4x−6x\frac { 7 x } { x ^ { 2 } + 4 x } - \frac { 6 } { x }x2+4x7x​−x6​ Please enter your answer as one fraction with the denominator factored completely.

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

Perform the indicated operation involving rational numbers. $\frac { 2 } { - 3 } \cdot \frac { - 15 } { 16 }$

The numbers $\frac { - 3 } { 7 }$ and $\frac { - 7 } { 3 }$ are multiplicative inverses.

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { a - 7 } { a } - \frac { 1 } { a + 7 }$ Please enter your answer as one fraction with the denominator factored completely and the numerator not factored.

Perform the indicated operation and express your answer in simplest form. $\frac { 7 n } { n ^ { 2 } - 25 } - \frac { 5 } { 2 n - 10 }$ Please enter your answer as one fraction with the denominator factored completely.

Solve the equation for the variable x . $y = \frac { 5 } { 6 } x + \frac { 3 } { 12 }$

Perform the indicated operations involving rational expressions. Match each expression with the corresponding answer. - $- \frac { 7 x ^ { 3 } y ^ { 3 } } { 8 }$

Perform the operation involving rational numbers. $\frac { 1 } { 4 } + \frac { 7 } { 8 } - \frac { 7 } { 16 }$

Express the rational number in reduced form. $\frac { 45 } { 54 }$

Simplify the rational expression. $\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 3 x }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { x - 3 } { 9 } + \frac { x + 9 } { 10 }$

Express the rational number in reduced form. $\frac { 65 } { - 78 }$

The least common denominator of $\frac { 7 } { x - 1 } + \frac { 3 } { 1 - x }$ is $x - 1$ .

Simplify the rational expression. $\frac { 64 x ^ { 4 } + 27 x } { 12 x ^ { 3 } - 63 x ^ { 2 } - 54 x }$

Perform the indicated operation involving rational numbers. Express final answer in reduced form. $\frac { - 3 } { 4 } \cdot \frac { 28 } { 39 }$

Solve the equation. $\frac { x } { x + 2 } + 3 = \frac { 7 } { x + 2 }$

Simplify the complex fraction. $\frac { - \frac { 5 } { x } - \frac { 10 } { x + 5 } } { \frac { 3 } { x ^ { 2 } + 5 x } + \frac { 3 } { x } }$

If the indicated quotient of rational expression is $- 1$ , then the numerator and denominator are opposites.

Simplify the rational expression. $\frac { x ^ { 4 } - 2 x ^ { 2 } - 48 } { 4 x ^ { 4 } + 29 x ^ { 2 } + 30 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 4 x } - \frac { 6 } { x }$ Please enter your answer as one fraction with the denominator factored completely.