Exam 6: Reducing Rational Expressions to Lowest Terms

Solve the following proportion.

Perform the indicated operation.

Reduce the following rational expression to lowest terms.

A water tank can be filled in 24 hours by an inlet pipe and emptied in 33 hours by an outlet pipe. How long will it take to fill the tank if both pipes are left open?

If is added to twice the reciprocal of a number, the result is 3. Find the number.

Perform the indicated operation.

An airplane flying against the wind travels 390 miles in the same amount of time it would take the same plane to travel 410 miles with the wind. If the wind speed is a constant 10 miles per hour, how fast would the plane travel in still air? __________ miles per hour

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.

Perform the indicated operation.

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 = __________

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 proportion.

Perform the indicated operation.

Perform the indicated operation.

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

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

Simplify inside the parentheses first, then multiply.

Reduce the following rational expression to lowest terms, if possible.

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

Solve the following proportion.