Exam 6: Rational Expressions and Equations

Multiply. - $\frac { x ^ { 3 } - 3 x ^ { 2 } + 5 x - 15 } { x ^ { 5 } - 2 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } } \cdot \frac { 4 x ^ { 3 } + 8 x ^ { 2 } + x + 2 } { 4 x ^ { 3 } - 12 x ^ { 2 } + x - 3 }$

(Multiple Choice)

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Question 101

Multiply. - $\frac { 2 p - 2 } { p } \cdot \frac { 9 p ^ { 2 } } { 8 p - 8 }$

(Multiple Choice)

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Question 102

Simplify the rational expression. - $\frac { 36 - k ^ { 2 } } { k ^ { 2 } - 15 k + 54 }$

(Multiple Choice)

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Question 103

Add or subtract. - $\frac { 5 } { x ^ { 2 } } - \frac { 6 } { x }$

(Multiple Choice)

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Question 104

Divide. - $\frac { 6 x ^ { 2 } + 6 x y - x y ^ { 2 } - y ^ { 3 } } { x ^ { 3 } + 6 x ^ { 2 } + x y ^ { 2 } + 6 y ^ { 2 } } \div \frac { x ^ { 3 } + 10 x + x ^ { 2 } y + 10 y } { x ^ { 3 } + 10 x + 6 x ^ { 2 } + 60 }$

(Multiple Choice)

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Question 105

Add or subtract. - $\frac { y + 5 } { y - 7 } - \frac { y + 5 } { y - 1 }$

(Multiple Choice)

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Question 106

Divide. - $\frac { 6 x - 2 x ^ { 2 } } { x ^ { 3 } - 27 } \div \frac { x } { x ^ { 2 } + 3 x + 9 }$

(Multiple Choice)

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Question 107

Multiply. - $\frac { x ^ { 3 } + x ^ { 2 } y + 3 x + 3 y } { 2 x ^ { 4 } + 6 x ^ { 2 } } \cdot \frac { 9 x ^ { 3 } } { 3 x ^ { 2 } - 3 y ^ { 2 } }$

(Multiple Choice)

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Question 108

Multiply. - $\frac { 2 x ^ { 2 } - 3 x - 9 } { 2 x ^ { 2 } - 2 x - 12 } \cdot \frac { 2 x ^ { 2 } + 10 x + 12 } { 8 x ^ { 2 } + 6 x - 9 }$

(Multiple Choice)

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Question 109

Divide. - $\frac { 35 x ^ { 2 } - 11 x y - 6 y ^ { 2 } } { 21 x ^ { 2 } + 41 x y + 10 y ^ { 2 } } \div \frac { 25 x ^ { 2 } - 45 x y + 18 y ^ { 2 } } { 35 x ^ { 2 } - 82 x y + 48 y ^ { 2 } }$

(Multiple Choice)

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Question 110

Determine the domain of the function. - $f ( x ) = \frac { 5 x - 8 } { x ^ { 2 } - 49 }$

(Multiple Choice)

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Question 111

Add or subtract. - $\frac { 7 } { 18 x } + \frac { 8 } { 3 x ^ { 2 } }$

(Multiple Choice)

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Question 112

Add or subtract. - $\frac { 4 x - 15 } { x ^ { 2 } - 2 x - 63 } + \frac { 6 - 3 x } { x ^ { 2 } - 2 x - 63 }$

(Multiple Choice)

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Question 113

Perform the indicated operations. - $\frac { 3 x ^ { 2 } - 7 x - 6 } { y ^ { 2 } + 2 y - 3 } \cdot \frac { y ^ { 2 } + 3 y - 4 } { 9 x ^ { 2 } + 9 x + 2 } \div \frac { 3 x ^ { 2 } - 8 x - 3 } { 6 x ^ { 2 } - 7 x - 3 }$

(Multiple Choice)

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Question 114

Multiply. - $\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }$

(Multiple Choice)

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Question 115

Add or subtract. - $\frac { 15 } { q - 7 } - \frac { 6 } { q - 7 }$

(Multiple Choice)

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Question 116

Multiply. - $\frac { z ^ { 3 } - 64 } { z ^ { 2 } - 3 z - 4 } \cdot \frac { 2 z ^ { 2 } + 11 z + 9 } { 11 z ^ { 2 } + 44 z + 176 }$

(Multiple Choice)

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Question 117

Simplify the rational expression. - $\frac { 22 x ^ { 2 } y ^ { 4 } - 16 x y + 4 x ^ { 5 } y ^ { 5 } } { 18 x ^ { 2 } y }$

(Multiple Choice)

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Question 118

Add or subtract. - $\frac { 3 x ^ { 2 } + 21 } { x - 7 } + \frac { - 4 x } { x - 7 } - \frac { 2 x ^ { 2 } + 6 x } { x - 7 }$

(Multiple Choice)

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Question 119

Determine the domain of the function. - $p ( x ) = \frac { 3 x ^ { 2 } - 5 x - 2 } { x ^ { 2 } - 4 }$

(Multiple Choice)

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Question 120

Multiply. - $\frac { x ^ { 3 } - 3 x ^ { 2 } + 5 x - 15 } { x ^ { 5 } - 2 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } } \cdot \frac { 4 x ^ { 3 } + 8 x ^ { 2 } + x + 2 } { 4 x ^ { 3 } - 12 x ^ { 2 } + x - 3 }$

Multiply. - $\frac { 2 p - 2 } { p } \cdot \frac { 9 p ^ { 2 } } { 8 p - 8 }$

Simplify the rational expression. - $\frac { 36 - k ^ { 2 } } { k ^ { 2 } - 15 k + 54 }$

Add or subtract. - $\frac { 5 } { x ^ { 2 } } - \frac { 6 } { x }$

Divide. - $\frac { 6 x ^ { 2 } + 6 x y - x y ^ { 2 } - y ^ { 3 } } { x ^ { 3 } + 6 x ^ { 2 } + x y ^ { 2 } + 6 y ^ { 2 } } \div \frac { x ^ { 3 } + 10 x + x ^ { 2 } y + 10 y } { x ^ { 3 } + 10 x + 6 x ^ { 2 } + 60 }$

Add or subtract. - $\frac { y + 5 } { y - 7 } - \frac { y + 5 } { y - 1 }$

Divide. - $\frac { 6 x - 2 x ^ { 2 } } { x ^ { 3 } - 27 } \div \frac { x } { x ^ { 2 } + 3 x + 9 }$

Multiply. - $\frac { x ^ { 3 } + x ^ { 2 } y + 3 x + 3 y } { 2 x ^ { 4 } + 6 x ^ { 2 } } \cdot \frac { 9 x ^ { 3 } } { 3 x ^ { 2 } - 3 y ^ { 2 } }$

Multiply. - $\frac { 2 x ^ { 2 } - 3 x - 9 } { 2 x ^ { 2 } - 2 x - 12 } \cdot \frac { 2 x ^ { 2 } + 10 x + 12 } { 8 x ^ { 2 } + 6 x - 9 }$

Divide. - $\frac { 35 x ^ { 2 } - 11 x y - 6 y ^ { 2 } } { 21 x ^ { 2 } + 41 x y + 10 y ^ { 2 } } \div \frac { 25 x ^ { 2 } - 45 x y + 18 y ^ { 2 } } { 35 x ^ { 2 } - 82 x y + 48 y ^ { 2 } }$

Determine the domain of the function. - $f ( x ) = \frac { 5 x - 8 } { x ^ { 2 } - 49 }$

Add or subtract. - $\frac { 7 } { 18 x } + \frac { 8 } { 3 x ^ { 2 } }$

Add or subtract. - $\frac { 4 x - 15 } { x ^ { 2 } - 2 x - 63 } + \frac { 6 - 3 x } { x ^ { 2 } - 2 x - 63 }$

Perform the indicated operations. - $\frac { 3 x ^ { 2 } - 7 x - 6 } { y ^ { 2 } + 2 y - 3 } \cdot \frac { y ^ { 2 } + 3 y - 4 } { 9 x ^ { 2 } + 9 x + 2 } \div \frac { 3 x ^ { 2 } - 8 x - 3 } { 6 x ^ { 2 } - 7 x - 3 }$

Multiply. - $\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }$

Add or subtract. - $\frac { 15 } { q - 7 } - \frac { 6 } { q - 7 }$

Multiply. - $\frac { z ^ { 3 } - 64 } { z ^ { 2 } - 3 z - 4 } \cdot \frac { 2 z ^ { 2 } + 11 z + 9 } { 11 z ^ { 2 } + 44 z + 176 }$

Simplify the rational expression. - $\frac { 22 x ^ { 2 } y ^ { 4 } - 16 x y + 4 x ^ { 5 } y ^ { 5 } } { 18 x ^ { 2 } y }$

Add or subtract. - $\frac { 3 x ^ { 2 } + 21 } { x - 7 } + \frac { - 4 x } { x - 7 } - \frac { 2 x ^ { 2 } + 6 x } { x - 7 }$

Determine the domain of the function. - $p ( x ) = \frac { 3 x ^ { 2 } - 5 x - 2 } { x ^ { 2 } - 4 }$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 6: Rational Expressions and Equations

Multiply. - 2p−2p⋅9p28p−8\frac { 2 p - 2 } { p } \cdot \frac { 9 p ^ { 2 } } { 8 p - 8 }p2p−2​⋅8p−89p2​

Simplify the rational expression. - 36−k2k2−15k+54\frac { 36 - k ^ { 2 } } { k ^ { 2 } - 15 k + 54 }k2−15k+5436−k2​

Add or subtract. - 5x2−6x\frac { 5 } { x ^ { 2 } } - \frac { 6 } { x }x25​−x6​

Add or subtract. - y+5y−7−y+5y−1\frac { y + 5 } { y - 7 } - \frac { y + 5 } { y - 1 }y−7y+5​−y−1y+5​

Divide. - 6x−2x2x3−27÷xx2+3x+9\frac { 6 x - 2 x ^ { 2 } } { x ^ { 3 } - 27 } \div \frac { x } { x ^ { 2 } + 3 x + 9 }x3−276x−2x2​÷x2+3x+9x​

Multiply. - x3+x2y+3x+3y2x4+6x2⋅9x33x2−3y2\frac { x ^ { 3 } + x ^ { 2 } y + 3 x + 3 y } { 2 x ^ { 4 } + 6 x ^ { 2 } } \cdot \frac { 9 x ^ { 3 } } { 3 x ^ { 2 } - 3 y ^ { 2 } }2x4+6x2x3+x2y+3x+3y​⋅3x2−3y29x3​

Multiply. - 2x2−3x−92x2−2x−12⋅2x2+10x+128x2+6x−9\frac { 2 x ^ { 2 } - 3 x - 9 } { 2 x ^ { 2 } - 2 x - 12 } \cdot \frac { 2 x ^ { 2 } + 10 x + 12 } { 8 x ^ { 2 } + 6 x - 9 }2x2−2x−122x2−3x−9​⋅8x2+6x−92x2+10x+12​

Determine the domain of the function. - f(x)=5x−8x2−49f ( x ) = \frac { 5 x - 8 } { x ^ { 2 } - 49 }f(x)=x2−495x−8​

Add or subtract. - 718x+83x2\frac { 7 } { 18 x } + \frac { 8 } { 3 x ^ { 2 } }18x7​+3x28​

Add or subtract. - 4x−15x2−2x−63+6−3xx2−2x−63\frac { 4 x - 15 } { x ^ { 2 } - 2 x - 63 } + \frac { 6 - 3 x } { x ^ { 2 } - 2 x - 63 }x2−2x−634x−15​+x2−2x−636−3x​

Multiply. - x2+12x+32x2+13x+36⋅x2+9xx2+6x−16\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }x2+13x+36x2+12x+32​⋅x2+6x−16x2+9x​

Add or subtract. - 15q−7−6q−7\frac { 15 } { q - 7 } - \frac { 6 } { q - 7 }q−715​−q−76​

Multiply. - z3−64z2−3z−4⋅2z2+11z+911z2+44z+176\frac { z ^ { 3 } - 64 } { z ^ { 2 } - 3 z - 4 } \cdot \frac { 2 z ^ { 2 } + 11 z + 9 } { 11 z ^ { 2 } + 44 z + 176 }z2−3z−4z3−64​⋅11z2+44z+1762z2+11z+9​

Simplify the rational expression. - 22x2y4−16xy+4x5y518x2y\frac { 22 x ^ { 2 } y ^ { 4 } - 16 x y + 4 x ^ { 5 } y ^ { 5 } } { 18 x ^ { 2 } y }18x2y22x2y4−16xy+4x5y5​

Add or subtract. - 3x2+21x−7+−4xx−7−2x2+6xx−7\frac { 3 x ^ { 2 } + 21 } { x - 7 } + \frac { - 4 x } { x - 7 } - \frac { 2 x ^ { 2 } + 6 x } { x - 7 }x−73x2+21​+x−7−4x​−x−72x2+6x​

Determine the domain of the function. - p(x)=3x2−5x−2x2−4p ( x ) = \frac { 3 x ^ { 2 } - 5 x - 2 } { x ^ { 2 } - 4 }p(x)=x2−43x2−5x−2​

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Multiply. - $\frac { 2 p - 2 } { p } \cdot \frac { 9 p ^ { 2 } } { 8 p - 8 }$

Simplify the rational expression. - $\frac { 36 - k ^ { 2 } } { k ^ { 2 } - 15 k + 54 }$

Add or subtract. - $\frac { 5 } { x ^ { 2 } } - \frac { 6 } { x }$

Add or subtract. - $\frac { y + 5 } { y - 7 } - \frac { y + 5 } { y - 1 }$

Divide. - $\frac { 6 x - 2 x ^ { 2 } } { x ^ { 3 } - 27 } \div \frac { x } { x ^ { 2 } + 3 x + 9 }$

Multiply. - $\frac { x ^ { 3 } + x ^ { 2 } y + 3 x + 3 y } { 2 x ^ { 4 } + 6 x ^ { 2 } } \cdot \frac { 9 x ^ { 3 } } { 3 x ^ { 2 } - 3 y ^ { 2 } }$

Multiply. - $\frac { 2 x ^ { 2 } - 3 x - 9 } { 2 x ^ { 2 } - 2 x - 12 } \cdot \frac { 2 x ^ { 2 } + 10 x + 12 } { 8 x ^ { 2 } + 6 x - 9 }$

Determine the domain of the function. - $f ( x ) = \frac { 5 x - 8 } { x ^ { 2 } - 49 }$

Add or subtract. - $\frac { 7 } { 18 x } + \frac { 8 } { 3 x ^ { 2 } }$

Add or subtract. - $\frac { 4 x - 15 } { x ^ { 2 } - 2 x - 63 } + \frac { 6 - 3 x } { x ^ { 2 } - 2 x - 63 }$

Multiply. - $\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }$

Add or subtract. - $\frac { 15 } { q - 7 } - \frac { 6 } { q - 7 }$

Multiply. - $\frac { z ^ { 3 } - 64 } { z ^ { 2 } - 3 z - 4 } \cdot \frac { 2 z ^ { 2 } + 11 z + 9 } { 11 z ^ { 2 } + 44 z + 176 }$

Simplify the rational expression. - $\frac { 22 x ^ { 2 } y ^ { 4 } - 16 x y + 4 x ^ { 5 } y ^ { 5 } } { 18 x ^ { 2 } y }$

Add or subtract. - $\frac { 3 x ^ { 2 } + 21 } { x - 7 } + \frac { - 4 x } { x - 7 } - \frac { 2 x ^ { 2 } + 6 x } { x - 7 }$

Determine the domain of the function. - $p ( x ) = \frac { 3 x ^ { 2 } - 5 x - 2 } { x ^ { 2 } - 4 }$