Exam 6: Reducing Rational Expressions to Lowest Terms

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.)

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

Simplify inside the parentheses first, then multiply.

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.

Reduce the following rational expression to lowest terms.

One number is 3 times as large as another. The sum of their reciprocals is . Find the two numbers.

Simplify the complex fraction.

Solve the following proportion.

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.

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.)

Solve the following proportion. x = __________

Simplify each term in the following sequence.

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

The first Ferris wheel was designed and built by George Ferris in 1893. It was a large wheel with a circumference of 785 feet. If one trip around the wheel takes 20 minutes, find the average speed of a rider on this wheel in miles per hour. Give the answer to two decimal places, if necessary. __________ miles per hour

Perform the indicated operation.

Simplify each term in the following sequence.

Tina is training for a biathlon. To train for the running portion of the race, she runs 14 miles each day, over the same course. The first 4 miles of the course is on level ground, while the last 10 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?

If is added to twice the reciprocal of a number, the result is 1. Find the number.

Tina is training for a biathlon. To train for the running portion of the race, she runs 5 miles each day, over the same course. The first 2 miles of the course is on level ground, while the last 3 miles is downhill. She runs 2 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? __________ miles per hour

Solve the following proportion.