Exam 6: Rational Expression and Equations

Divide using synthetic division: $\frac { 5 x ^ { 3 } + 9 x ^ { 2 } - 6 x - 2 } { x + 2 }$

Solve the equation and check the result. If the equation has no solution, answer none . $\frac { 7 } { 25 } - \frac { 1 } { 5 } = \frac { 1 } { b }$

Solve the proportion. $\frac { 3 } { c } = \frac { c - 3 } { 6 }$

Which of the following is a factor of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 8$

If $P ( k ) = 0$ , then $x - k$ is a _________ of $P ( x )$

The Washington Monument shown below casts a shadow of $169 \frac { 1 } { 2 }$ feet at the same time as a 5-foot-tall tourist casts a shadow of $1 \frac { 1 } { 2 }$ feet. Find the height of the monument.

Perform the indicated operation. Simplify, if possible. $\frac { 25 y ^ { 2 } + 40 y + 16 } { 12 y + 18 } \div \frac { 10 y ^ { 2 } - 7 y - 12 } { 4 y ^ { 2 } - 9 }$

Perform the operations and simplify the result when possible. $\frac { 3 } { x ^ { 2 } - 4 x - 5 } - \frac { x } { 3 x ^ { 2 } - 13 x - 10 }$

On average, it takes a teacher 42 minutes to grade a set of quizzes. It takes her teacher's aide twice as long to do the same grading. How long will it take if they work together to grade a set of quizzes?

Simplify. Write the answer using positive exponents. $\frac { 4 x ^ { 2 } y ^ { 4 } } { 8 x ^ { 6 } y ^ { 3 } }$

Divide using synthetic division: $\frac { x ^ { 3 } - 2 x ^ { 2 } - 9 } { x + 3 }$

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = 2 x ^ { 3 } + x + 1 ; k = 3$

It takes a grounds keeper 45 minutes to prepare a softball field for a game. It takes his assistant 55 minutes to prepare the same field. How long will it take if they work together to prepare the field? _________ min

Princess Allison can fill the moat around her enchanted castle in 6 hours and her evil wicked stepsister could fill it in 8 hours. Princess Allison's godmother said if they worked together they would live happily ever after. How long would it take to fill the moat if they work together?

Solve the proportion. $\frac { r - 2 } { 5 } = \frac { r } { 7 }$

If one outlet pipe can drain a pipe in 24 hours and another pipe can drain the tank in 36 hours, how long will it take for both pipes to drain the tank?

Perform the operations and simplify the result when possible. $\frac { 3 x } { 2 x - 1 } + \frac { x + 2 } { 3 x + 2 } - \frac { 4 x } { 6 x ^ { 3 } + x ^ { 2 } - 2 x }$

Perform the operations and simplify the result when possible. $\frac { s + 6 } { s - 6 } - \frac { s - 6 } { s + 6 }$

Solve: $\frac { 4 } { 3 x } - \frac { 3 } { 2 x } = 3 - \frac { 9 } { 18 x }$

Solve the problem by writing a variation model. The costs of a trucking company vary jointly with the number of trucks in service and the number of hours they are used. When 3 trucks are used for 7 hours each, the costs are $1,533. Find the costs of using 9 trucks, each for 13 hours.