Exam 7: Rational Expressions

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 = __________

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

Multiply the expressions.

Assume varies inversely with the square of . If when find when is 6.

Perform the indicated operation.

Simplify each term in the following sequence.

Perform the indicated operation.

Solve the following proportion.

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.

The resistance in an electric circuit varies directly with the voltage . If when find when

Assume varies inversely with the square of . If when find when is .

Perform the indicated operation.

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 proportion.

An airplane flying against the wind travels 380 miles in the same amount of time it would take the same plane to travel 400 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

Tina is training for a biathlon. To train for the running portion of the race, she runs 8 miles each day, over the same course. The first 2 miles of the course is on level ground, while the last 6 miles is downhill. She runs 3 miles per hour slower on level ground than she runs downhill. If the complete course takes 1 hour, how fast does she run on the downhill part of the course?

Perform the indicated operation.

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

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