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Exam 9: Rational Expressions

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Question 141

Multiple Choice

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Solve the equation. $\frac { x } { 5 x ^ { 2 } + 6 x } - \frac { x } { 5 x ^ { 2 } + 11 x + 6 } = \frac { 4 } { x ^ { 2 } + x }$

A) $x = - \frac { 19 } { 24 }$
B) $x = - \frac { 24 } { 19 }$
C) $x = \frac { 24 } { 19 }$

D) A) and B)
E) A) and C)

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Question 142

Multiple Choice

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Perform the indicated operation. $\frac { 5 } { x ^ { 2 } + 2 } - \frac { 2 } { x ^ { 2 } + 4 x - 5 }$

A) $\frac { 3 x ^ { 2 } + 20 x - 29 } { \left( x ^ { 2 } + 2 \right) ( x + 5 ) ( x - 1 ) }$
B) $\frac { 3 x ^ { 2 } + 20 x - 29 } { \left( x ^ { 2 } + 2 \right) ( x - 5 ) ( x + 1 ) }$
C) $\frac { x ^ { 2 } + 20 x - 29 } { \left( x ^ { 2 } + 2 \right) ( x - 5 ) ( x + 1 ) }$
D) $\frac { x ^ { 2 } + 20 x - 29 } { \left( x ^ { 2 } + 2 \right) ( x + 5 ) ( x - 1 ) }$

E) A) and C)
F) All of the above

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Question 143

Short Answer

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Add the rational expressions. Be sure to express your answer in simplest form. $\frac { 2 x } { x - 1 } + \frac { 16 } { x - 1 }$

Solve the equation. $\frac { 4 } { 3 x - 10 } = \frac { 6 } { 2 x + 10 }$

The ratio of male students to female students at a certain university is 8 to 5. If there is a total of 13,000 students, find the number of male students and the number of female students. __________ male students __________ female students

Perform the indicated operation and express your answer in simplest form. $\frac { 17 n ^ { 2 } } { n ^ { 4 } - 81 } - \frac { n } { n ^ { 2 } - 9 } + \frac { 1 } { n + 3 }$ Please enter your answer as one fraction with the denominator factored completely.

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 3 x ^ { 7 } y ^ { 7 } } { 4 x ^ { 8 } y ^ { 6 } } \div \frac { 24 } { 12 x ^ { 7 } }$

Solve each equation for the variable y . $- \frac { 5 } { x - 20 } = \frac { 9 } { y - 1 }$

Simplify the rational expression. $\frac { - 20 y ^ { 3 } } { 45 x y ^ { 2 } }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 2 } { 8 x - 1 } - \frac { 1 } { 4 x + 2 }$

Solve the equation. $\frac { 2 } { 3 x } + \frac { 5 } { 6 } = \frac { 7 } { 6 x }$

In a division problem, change all division to multiplication in order to simplify.

The perimeter of a rectangle is 126 centimeters. If the ratio of its width to its length is 4 to 5, find the dimensions of the rectangle. __________ cm by ___________ cm

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

Simplify the complex fraction. $\frac { \frac { - 2 } { x } - \frac { 4 } { x + 2 } } { \frac { 7 } { x ^ { 2 } + 2 x } + \frac { 7 } { x } }$

Solve the equation for the variable y . $- \frac { 7 } { x - 14 } = \frac { 8 } { y - 1 }$

A sum of $2,000 is to be divided between two people in the ratio of 3 to 5. How much does each person receive?