Exam 7: Rational Expressions

Solve the following proportion.

To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.)

Simplify the complex fraction.

One plane can travel 40 miles per hour faster than another. One of them goes 550 miles in the same time it takes the other to go 450 miles. What are their speeds? _____ , _____ miles per hour

Simplify inside the parentheses first, then multiply.

Reduce the following rational expression to lowest terms.

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.

A baseball player gets 7 hits in the first 28 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 40 games?

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. x = __________

Simplify the complex fraction.

Perform the indicated operation.

Solve the following proportion.

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

Perform the indicated operation.

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. x = __________

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.

Solve the following proportion.

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

A bathtub can be filled by the cold water faucet in 17 minutes and by the hot water faucet in 18 minutes. The drain can empty the tub in 9 minutes. Can the tub be filled if both faucets and the drain are open? Answer yes or no .