8 1 MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Vocabulary

8. 1 MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS

Vocabulary Rational Expression – a ratio of 2 polynomial expressions. A rational expression is undefined when the denominator is equal to zero.

Example 1: Simplify Under what conditions is the expression undefined?

Example 2: Simplify For what value(s) of p is the expression undefined?

Example 3: Simplify

Example 4: Simplify

With polynomials, factor first! Example 5: Simplify

Example 6: Simplify

Example 7: Simplify.

Example 8 Simplify

Example 9: Simplify.

Example 10: Simplify.

Complex Fractions Example 11: Simplify

Complex Fractions Example 12: Simplify

Complex Fractions Example 13: Simplify

Example 14 You are considering buying a swimming pool and have narrowed the choices to two—one that is circular and one that is rectangular. The width of the rectangular pool is three times its depth. Its length is 6 feet more than its width. The circular pool has a diameter that is twice the width of the rectangular pool, and it is 2 feet deeper. a. Find the ratio of the volume of the circular pool to the volume of the rectangular pool. b. The volume of the rectangular pool is 2592 cubic feet. How many gallons of water are needed to fill the circular pool if 1 gallon is approximately 0. 134 cubic foot?