Exam 7: Rational Expressions and Equations

Mary invested same amount of money in two bond funds for 1 year. They pay interest at rates that differ by 4%. Money invested in the first fund earns $360, and money invested in the second fund earns $600. Find the bigger rate of interest.

(Multiple Choice)

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Question 61

Simplify the rational expression. $\frac { 16 x ^ { 2 } y + 32 x y ^ { 2 } - 48 y ^ { 3 } } { 60 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 3 } }$

(Multiple Choice)

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Question 62

Perform the indicated operation. Simplify the answer if possible. $\frac { 9 s + 4 } { 5 s b } - \frac { 4 s + 4 } { 5 s b }$

(Essay)

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Question 63

Which value of x makes the rational expression $\frac { x ^ { 2 } - 5 x } { x ^ { 2 } + 9 }$ undefined?

(Multiple Choice)

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Question 64

A homeowner estimates that it will take her 8 days to roof her house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer?

(Multiple Choice)

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Question 65

Perform the indicated operation and simplify. $\frac { 3 b ^ { 2 } - 14 b - 5 } { b ^ { 2 } - 25 } \cdot \frac { 2 b ^ { 2 } + 8 b - 10 } { 3 b ^ { 2 } + 10 b + 3 }$

(Multiple Choice)

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Question 66

Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. $\frac { 8 k + 8 c } { k ^ { 2 } + k c }$

(Multiple Choice)

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Question 67

Evaluate the following expression for the given value of the variable. $\frac { x - 6 } { 6 - x }$ for $x = 1$

(Multiple Choice)

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Question 68

Perform the indicated division and express your answer in simplest form. $\frac { 26 x z } { 214 } \div 6 x$

(Essay)

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Question 69

The focal length f of a lens is given by the formula $\frac { 1 } { f } = \frac { 4 } { d 1 } + \frac { 3 } { d 2 }$ where d1 is the distance from the object to the lens and d2 is the distance from the lens to the image. Solve the formula for f .

(Essay)

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Question 70

Express the sentence as a formula. Assume that $k$ is a constant of variation. For a fixed area, the length l of a rectangle varies inversely with its width $y$ .

(Multiple Choice)

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Question 71

Build the fraction into an equivalent fraction with the indicated denominator. $\frac { 4 } { 9 } ; 45 u$

(Essay)

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Question 72

Perform the indicated operation and simplify. $\frac { x ^ { 2 } - 9 } { x ^ { 2 } - 81 } \div \frac { x + 3 } { x + 9 }$

(Multiple Choice)

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Question 73

Two denominators are given. Find the LCD. t² $-$ 7 t $-$ 8, t ² $-$ 64

(Essay)

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Question 74

Find any real numbers x which make $\frac { x - 2 } { x ^ { 2 } - 3 x - 10 }$ undefined.

(Multiple Choice)

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Question 75

Mary invested same amount of money in two bond funds for 1 year. They pay interest at rates that differ by 4%. Money invested in the first fund earns $360, and money invested in the second fund earns $600. Find the bigger rate of interest.

Simplify the rational expression. $\frac { 16 x ^ { 2 } y + 32 x y ^ { 2 } - 48 y ^ { 3 } } { 60 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 3 } }$

Perform the indicated operation. Simplify the answer if possible. $\frac { 9 s + 4 } { 5 s b } - \frac { 4 s + 4 } { 5 s b }$

Which value of x makes the rational expression $\frac { x ^ { 2 } - 5 x } { x ^ { 2 } + 9 }$ undefined?

A homeowner estimates that it will take her 8 days to roof her house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer?

Perform the indicated operation and simplify. $\frac { 3 b ^ { 2 } - 14 b - 5 } { b ^ { 2 } - 25 } \cdot \frac { 2 b ^ { 2 } + 8 b - 10 } { 3 b ^ { 2 } + 10 b + 3 }$

Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. $\frac { 8 k + 8 c } { k ^ { 2 } + k c }$

Evaluate the following expression for the given value of the variable. $\frac { x - 6 } { 6 - x }$ for $x = 1$

Perform the indicated division and express your answer in simplest form. $\frac { 26 x z } { 214 } \div 6 x$

The focal length f of a lens is given by the formula $\frac { 1 } { f } = \frac { 4 } { d 1 } + \frac { 3 } { d 2 }$ where d1 is the distance from the object to the lens and d2 is the distance from the lens to the image. Solve the formula for f .

Express the sentence as a formula. Assume that $k$ is a constant of variation. For a fixed area, the length l of a rectangle varies inversely with its width $y$ .

Build the fraction into an equivalent fraction with the indicated denominator. $\frac { 4 } { 9 } ; 45 u$

Perform the indicated operation and simplify. $\frac { x ^ { 2 } - 9 } { x ^ { 2 } - 81 } \div \frac { x + 3 } { x + 9 }$

Two denominators are given. Find the LCD. t² $-$ 7 t $-$ 8, t ² $-$ 64

Find any real numbers x which make $\frac { x - 2 } { x ^ { 2 } - 3 x - 10 }$ undefined.

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Factoring and Quadratic Equations

Roots and Radicals

Quadratic Equations

Filters

Exam 7: Rational Expressions and Equations

Mary invested same amount of money in two bond funds for 1 year. They pay interest at rates that differ by 4%. Money invested in the first fund earns $360, and money invested in the second fund earns $600. Find the bigger rate of interest.

Simplify the rational expression. 16x2y+32xy2−48y360x3y−40x2y2−20xy3\frac { 16 x ^ { 2 } y + 32 x y ^ { 2 } - 48 y ^ { 3 } } { 60 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 3 } }60x3y−40x2y2−20xy316x2y+32xy2−48y3​

Perform the indicated operation. Simplify the answer if possible. 9s+45sb−4s+45sb\frac { 9 s + 4 } { 5 s b } - \frac { 4 s + 4 } { 5 s b }5sb9s+4​−5sb4s+4​

Which value of x makes the rational expression x2−5xx2+9\frac { x ^ { 2 } - 5 x } { x ^ { 2 } + 9 }x2+9x2−5x​ undefined?

A homeowner estimates that it will take her 8 days to roof her house. A professional roofer estimates that he could roof the house in 5 days. How long will it take if the homeowner helps the roofer?

Perform the indicated operation and simplify. 3b2−14b−5b2−25⋅2b2+8b−103b2+10b+3\frac { 3 b ^ { 2 } - 14 b - 5 } { b ^ { 2 } - 25 } \cdot \frac { 2 b ^ { 2 } + 8 b - 10 } { 3 b ^ { 2 } + 10 b + 3 }b2−253b2−14b−5​⋅3b2+10b+32b2+8b−10​

Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. 8k+8ck2+kc\frac { 8 k + 8 c } { k ^ { 2 } + k c }k2+kc8k+8c​

Evaluate the following expression for the given value of the variable. x−66−x\frac { x - 6 } { 6 - x }6−xx−6​ for x=1x = 1x=1

Perform the indicated division and express your answer in simplest form. 26xz214÷6x\frac { 26 x z } { 214 } \div 6 x21426xz​÷6x

The focal length f of a lens is given by the formula 1f=4d1+3d2\frac { 1 } { f } = \frac { 4 } { d 1 } + \frac { 3 } { d 2 }f1​=d14​+d23​ where d1 is the distance from the object to the lens and d2 is the distance from the lens to the image. Solve the formula for f .

Express the sentence as a formula. Assume that kkk is a constant of variation. For a fixed area, the length l of a rectangle varies inversely with its width yyy .

Build the fraction into an equivalent fraction with the indicated denominator. 49;45u\frac { 4 } { 9 } ; 45 u94​;45u

Perform the indicated operation and simplify. x2−9x2−81÷x+3x+9\frac { x ^ { 2 } - 9 } { x ^ { 2 } - 81 } \div \frac { x + 3 } { x + 9 }x2−81x2−9​÷x+9x+3​

Two denominators are given. Find the LCD. t 2 −-− 7 t −-− 8, t 2 −-− 64

Find any real numbers x which make x−2x2−3x−10\frac { x - 2 } { x ^ { 2 } - 3 x - 10 }x2−3x−10x−2​ undefined.

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Factoring and Quadratic Equations

Roots and Radicals

Quadratic Equations

Filters

Simplify the rational expression. $\frac { 16 x ^ { 2 } y + 32 x y ^ { 2 } - 48 y ^ { 3 } } { 60 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 3 } }$

Perform the indicated operation. Simplify the answer if possible. $\frac { 9 s + 4 } { 5 s b } - \frac { 4 s + 4 } { 5 s b }$

Which value of x makes the rational expression $\frac { x ^ { 2 } - 5 x } { x ^ { 2 } + 9 }$ undefined?

Perform the indicated operation and simplify. $\frac { 3 b ^ { 2 } - 14 b - 5 } { b ^ { 2 } - 25 } \cdot \frac { 2 b ^ { 2 } + 8 b - 10 } { 3 b ^ { 2 } + 10 b + 3 }$

Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. $\frac { 8 k + 8 c } { k ^ { 2 } + k c }$

Evaluate the following expression for the given value of the variable. $\frac { x - 6 } { 6 - x }$ for $x = 1$

Perform the indicated division and express your answer in simplest form. $\frac { 26 x z } { 214 } \div 6 x$

The focal length f of a lens is given by the formula $\frac { 1 } { f } = \frac { 4 } { d 1 } + \frac { 3 } { d 2 }$ where d1 is the distance from the object to the lens and d2 is the distance from the lens to the image. Solve the formula for f .

Express the sentence as a formula. Assume that $k$ is a constant of variation. For a fixed area, the length l of a rectangle varies inversely with its width $y$ .

Build the fraction into an equivalent fraction with the indicated denominator. $\frac { 4 } { 9 } ; 45 u$

Perform the indicated operation and simplify. $\frac { x ^ { 2 } - 9 } { x ^ { 2 } - 81 } \div \frac { x + 3 } { x + 9 }$

Two denominators are given. Find the LCD. t² $-$ 7 t $-$ 8, t ² $-$ 64

Find any real numbers x which make $\frac { x - 2 } { x ^ { 2 } - 3 x - 10 }$ undefined.