Exam 7: Rational Expressions

Solve the following proportion. x = __________

The following problem involves some factoring by grouping. Remember, before you can divide out factors common to the numerator and denominator of a product, you must factor completely.

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. y = __________

A water faucet can fill a sink in 8 minutes, whereas the drain can empty it in 4 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open? __________ minutes

One number is 3 times as large as another. The sum of their reciprocals is . Find the two numbers.

A baseball player gets 8 hits in the first 40 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 85 games? __________ hits

The pressure exerted by a gas on the container in which it is held varies inversely with the volume of the container. A pressure of 50 pounds per square inch is exerted on a container of volume 4 cubic feet. What is the pressure on a container whose volume is 10 cubic feet?

Simplify the complex fraction.

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. a = __________

If varies directly with and if when find when is .

Perform the indicated operation.

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

Perform the indicated operation.

The amount of money M a woman makes per week varies directly with the number of hours h she works per week. If she works 10 hours and earns $143, how much does she make if she works 15 hours? M = $__________

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.

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.

Simplify the complex fraction.

Perform the indicated operation.

A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water faucet in 14 minutes. How long does it take to fill the tub if both faucets are open? Give the answer in minutes.

An economy car travels 261 miles on 4.5 gallons of gas. Give the average fuel consumption of the car in miles per gallon.