Exam 6: Reducing Rational Expressions to Lowest Terms

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 = __________

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.

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

Solve the following proportion.

A water faucet can fill a sink in 10 minutes, whereas the drain can empty it in 8 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open?

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

To train for the running of a triathlon, Jerri jogs 1 hour each day over the same 9-mile course. Five miles of the course is downhill, whereas the other 4 miles is on level ground. Jerri figures that she runs 2 miles per hour faster downhill than she runs on level ground. Find the rate at which Jerri runs on level ground. __________ miles per hour

Perform the indicated operation.

Simplify the complex fraction.

Simplify the complex fraction.

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

Solve the following proportion.

Solve the following proportion.

Perform the indicated operation.

Graph and on the same coordinate system. At what points do the two graphs intersect?

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.

Simplify the complex fraction.

Write the ratio as a fraction in lowest terms. to