Exam 9: Rational Expressions

Perform the indicated operation and express your answer in simplest form. $\frac { 4 } { x } - \frac { 3 x + 19 } { x ^ { 2 } + 5 x } + \frac { x } { x + 5 }$ Please enter your answer as one fraction with the denominator factored completely.

Perform the operation involving rational numbers. Be sure to express your answer in reduced form. $\frac { 4 } { 8 } + \frac { 1 } { 7 }$

Perform the indicated operation. $\frac { t + 6 } { 2 t + 1 } - \frac { 3 t ^ { 2 } + 1 t + 6 } { 2 t ^ { 2 } + 3 t + 1 } + \frac { t + 2 } { t + 1 }$

A 24-foot board is to be cut into two pieces whose lengths are in the ratio of 5 to 3. Find the lengths of the two pieces.

Perform the indicated operation involving rational expressions. Express final answer in simplest form. $\frac { 2 x ^ { 7 } y ^ { 7 } } { 3 x ^ { 8 } y ^ { 6 } } \cdot \frac { 9 x ^ { 7 } } { 8 }$

Perform the indicated operation involving rational expressions. $\frac { 16 n - 16 - 4 n ^ { 2 } } { 50 n - 125 - 5 n ^ { 2 } } \cdot \frac { 150 n - 375 - 15 n ^ { 2 } } { 144 - 96 n + 16 n ^ { 2 } }$

The equation $\frac { 3 x } { x + 2 } = \frac { 9 } { x + 5 } + x$ is a proportion.

Solve the equation. $\frac { x } { x - 6 } - 3 = \frac { 6 } { x - 6 }$

Perform the indicated operation and express your answer in simplest form. $\frac { 3 a } { 24 a ^ { 2 } - 6 a - 3 } + \frac { 1 } { 6 a ^ { 2 } + 15 a - 9 }$

Solve the equation. $\frac { x } { x + 3 } - 2 = \frac { 9 } { x - 9 }$

Perform the indicated operation. $\frac { 17 n ^ { 2 } } { n ^ { 4 } - 81 } - \frac { n } { n ^ { 2 } - 9 } + \frac { 1 } { n + 3 }$

The expression $\frac { m - 3 } { 5 } - \frac { m + 2 } { 5 }$ is equivalent to $- 1$ .

Solve the equation. $\frac { x } { x + 6 } - 2 = \frac { 18 } { x - 18 }$

Perform the indicated operation. $\frac { 16 x + 13 } { x ^ { 2 } - 4 } - \frac { 3 } { x - 2 }$

Simplify the rational expression. $\frac { 4 x - 7 } { 7 - 4 x }$

Perform the indicated operation involving rational expressions. $\frac { 2 x ^ { 9 } y ^ { 9 } } { 3 x ^ { 10 } y ^ { 8 } } \div \frac { 26 } { 9 x ^ { 9 } }$

Solve each equation. Match each equation with the corresponding solution. - $n = 1.75$

Perform the indicated operation involving rational numbers. $\frac { 3 } { 4 } \cdot \frac { 44 } { 39 }$

Perform the indicated operation involving rational expressions. $\frac { 8 x ^ { 8 } y ^ { 8 } } { 9 x ^ { 9 } y ^ { 7 } } \cdot \frac { 99 x ^ { 8 } } { 32 y } \div \frac { y ^ { 7 } } { 4 x }$

Perform the indicated operation. $\frac { 25 } { x ^ { 2 } - 3 x - 10 } - \frac { 9 } { x - 5 } - \frac { 2 } { x + 2 }$