Exam 7: Rational Expressions

The sum of the reciprocals of two consecutive integers is . Find the two integers.

Solve the following proportion.

If varies directly with and if when find when is 3.

A bathtub can be filled by the cold water faucet in 10 minutes and by the hot water faucet in 11 minutes. The drain can empty the tub in 4 minutes. Can the tub be filled if both faucets and the drain are open?

Simplify the complex fraction.

Reduce the following rational expression to lowest terms.

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

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.

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

Simplify the complex fraction.

If varies directly with and if when find when is 11.

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 each term in the following sequence.

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.

The numerator of a certain fraction is 1 more than the denominator. If is added to the fraction, the result is 2. Find the fraction.

The sum of a number and its reciprocal is . Find the number.

Perform the indicated operation.

If varies inversely with and if when find when is 10. = __________

Simplify the complex fraction.

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