Exam 6: Reducing Rational Expressions to Lowest Terms

One car travels 180 miles in the same amount of time it takes a second car traveling 6 miles per hour slower than the first to go 162 miles. What are the speeds of the cars?

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.

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

Solve the following proportion. x = __________

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

Simplify inside the parentheses first, then multiply.

Simplify the complex fraction.

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.

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.

Reduce the following rational expressions to lowest terms.

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

One plane can travel 10 miles per hour faster than another. One of them goes 400 miles in the same time it takes the other to go 375 miles. What are their speeds? _____ , _____ miles per hour

A solution contains 15 milliliters of alcohol and 20 milliliters of water. If another solution is to have the same concentration of alcohol in water but is to contain 32 milliliters of water, how much alcohol must it contain? __________ milliliters

Perform the indicated operation.

Perform the indicated operation.

Solve the following proportion.

Reduce the following rational expression to lowest terms.