Exam 6: Rational Expressions and Equations

Solve the problem. -A contractor finds that it takes Sam Tockett 9 hours to construct a wall of a certain size. It takes Jim Lowell 6 hours to construct the same wall. How long would it take if they worked together?

Add, first finding the LCD. Simplify, if possible. - $\frac { 7 } { 10 } + \frac { 3 } { 5 }$

Solve. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft Apart?

Add. Simplify, if possible. - $\frac { 4 } { y ^ { 2 } - 3 y + 2 } + \frac { 6 } { y ^ { 2 } - 1 }$

Add. Simplify, if possible. - $\frac { 3 } { ( x + 8 ) ^ { 2 } } + \frac { 7 } { x + 8 }$

Solve the problem. -A machine can fill 4551 cartons of milk in 0.6 hour. How many cartons of milk can it fill per hour?

Solve the equation. - $\frac { 7 } { x } = \frac { 6 } { x } + 6$

Subtract. Simplify, if possible. - $\frac { 7 } { 2 x - 3 } - \frac { 5 } { 3 - 2 x }$

Multiply. Do not simplify. - $\frac { x - 9 } { 5 - x } \cdot \frac { - 1 } { - 1 }$

Subtract. Simplify, if possible. - $\frac { 12 } { q - 6 } - \frac { 9 } { q - 6 }$

Simplify. - $\frac { y ^ { 2 } + 2 y } { y ^ { 2 } + 9 y }$

Answer the question. -For $x \neq 5$ , the rational expression $\frac { 8 ( x - 5 ) } { x - 5 }$ is equal to 8 . Can the same be said for $\frac { 8 x - 5 } { x - 5 }$ ? Explain why or why not.

Add. Simplify, if possible. - $\frac { x + 7 } { x - 3 } + \frac { x - 5 } { 3 - x } + \frac { 4 ( x + 1 ) } { x - 3 }$

Multiply and, if possible, simplify. - $\frac { 8 p - 8 } { p } \cdot \frac { 7 p ^ { 2 } } { 9 p - 9 }$

Find an equation of variation in which y varies inversely as x and the following is true. - $y = 5$ , when $x = 19$

Solve the equation. - $\frac { 9 } { x + 5 } = \frac { 6 } { x }$

Add. Simplify, if possible. - $\frac { 5 x + 5 } { 2 x - 3 } + \frac { 4 - 7 x } { - 3 + 2 x }$

Solve. -The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 41,000 mi has $\frac { 9 } { 32 }$ in of tread left. How much tread will be left on a tire that has traveled 82,000 mi? Express the answer as a fraction in simplest form.

Simplify. - $\frac { \frac { 1 } { m } + \frac { 1 } { z } } { \frac { 1 } { m } - \frac { 1 } { z } }$

Solve the equation. - $x + \frac { 40 } { x } = 14$