Exam 6: Reducing Rational Expressions to Lowest Terms

Solve the following proportion.

A boat travels 45 miles up the river in the same amount of time it takes to travel 85 miles down the same river. If the current is 4 miles per hour, what is the speed of the boat in still water? d r t Upstream Downstream

Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable. x = __________

Solve the following proportion. x = __________

Solve the following proportion. x = __________

Multiply the expressions.

If a bank charges $6.00 per month and $0.12 per check for one of its checking accounts, then the total monthly cost to write x checks is , and the average cost of each of the x checks written is Compare these two formulas by filling in the following table. Round to the nearest cent.

A sink can be filled by the cold water faucet in 6 minutes. The drain can empty a full sink in 8 minutes. If the sink is empty and both the cold water faucet and the drain are open, how long will it take the sink to overflow?

A water faucet can fill a sink in 8 minutes, whereas the drain can empty it in 6 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open? __________ minutes

Simplify the complex fraction.

Perform the indicated operation.

Simplify the complex fraction.

Simplify the expression. Work inside parentheses first, and then divide out common factors.

Reduce the following rational expression to lowest terms.

Multiply the expressions.

Travis paddles his kayak in the harbor at Morro Bay, California, where the incoming tide has caused a current in the water. From the point where he enters the water, he paddles 4 miles against the current, then turns around and paddles 4 miles back to where he started. His average speed when paddling with the current is 6 miles per hour faster than his speed against the current. If the complete trip (out and back) takes him 1.4 hours, find his average speed when he paddles against the current. __________ miles per hour

Perform the indicated operation.

Perform the indicated operation. Reduce your answer to lowest terms.

One car travels 490 miles in the same amount of time it takes a second car traveling 5 miles per hour slower than the first to go 455 miles. What are the speeds of the cars? _____ , _____ miles per hour

Solve the following equation. If impossible, answer no solution . Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.