Exam 9: Rational Expressions

Perform the indicated operation and express your answer in simplest form. $\frac { t + 18 } { 2 t + 3 } - \frac { 3 t ^ { 2 } + 3 t + 54 } { 2 t ^ { 2 } + 9 t + 9 } + \frac { t + 1 } { t + 3 }$ Please enter your answer as one fraction with the denominator factored completely.

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { n - 4 } { 9 } - \frac { n - 7 } { 12 }$

A ratio is the comparison of two numbers by division.

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

Recall that the indicated quotient of a polynomial and its opposite is $-$ 1. For example, $\frac { x - 2 } { 2 - x }$ simplifies to $-$ 1. Keep this idea in mind as you add or subtract the following rational expression. $\frac { 5 } { x - 5 } - \frac { x } { x - 5 } + 7$

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 5 } { 9 } - \frac { 3 } { 8 }$

Simplify the rational expression. $\frac { - 4 x ^ { 3 } y } { - 6 x y ^ { 4 } }$

Perform the indicated operation involving rational numbers. Express final answer in reduced form. $\left( - \frac { 5 } { 6 } \right) \div \frac { 40 } { 66 }$

Solve the equation. $2 + \frac { 4 } { n - 2 } = \frac { 8 } { n ^ { 2 } - 2 n }$

Simplify the rational expression. $\frac { 3 n ^ { 2 } - 14 n - 5 } { 7 n ^ { 2 } - 37 n + 10 }$

Solve the equation. $2 + \frac { 8 } { t - 7 } = \frac { 8 } { t ( t - 7 ) }$

Simplify the complex fraction. $10 + \frac { x } { 10 + \frac { 10 } { x } }$

A 5-foot board is to be cut into two pieces whose lengths are in the ratio of 3 to 2. Find the lengths of the two pieces. Longer piece __________ ft. Shorter piece __________ ft.

An inlet pipe can fill a tank in 10 minutes. A drain can empty the tank in 15 minutes. If the tank is empty and both the pipe and drain are open, how long will it take before the tank overflows?

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 3 } { 9 } - \frac { 2 } { 7 }$

Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 x } { x - 1 } - 2$

Simplify the rational expression. $\frac { 5 n ^ { 2 } - 29 n - 6 } { 5 n ^ { 2 } - 32 n + 12 }$

Add the rational expressions. Be sure to express your answer in simplest form. $\frac { a - 4 } { a } - \frac { 4 } { a + 7 }$

Perform the indicated operations involving rational expressions. Express the final answer in simplest form. $\frac { 4 n ^ { 2 } + 20 n - 24 } { 3 n ^ { 2 } + 10 n - 48 } \cdot \frac { 6 n ^ { 2 } - n - 40 } { 6 n ^ { 2 } + 9 n - 15 }$

Perform the indicated operation. $\frac { 7 n } { n ^ { 2 } - 25 } - \frac { 5 } { 2 n - 10 }$