Multiplying and Dividing Rational Expressions Section 9.2: Multiplying and Dividing Rational Expressions

9.2 Lecture Guide: Multiplying and Dividing Rational Expressions Objective 1: Multiply and divide rational expressions.

Algebraically Verbally Algebraic Example Multiplying Rational Expressions Algebraically Verbally Algebraic Example If A, B, C and D are real polynomials and and then _______________ the numerators and the denominators. Then write the product as a single fraction, indicating the product of the numerators and the product of the denominators. _______________ this fraction by dividing the numerator and the denominator by any common nonzero factors.

Dividing Rational Expressions Algebraically Verbally Algebraic Example If A, B, C and D are real polynomials and and then Rewrite the division problem as the product of the dividend and the _______________ of the divisor. Perform the multiplication using the rule for multiplying rational expressions.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 1.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 2.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 3.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 4.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 5.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 6.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 7.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 8.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 9.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 10.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 11.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 12.

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero. 13.

Determine the unknown expression in each equation. 14.

Determine the unknown expression in each equation. 15.

16. The number of items that a factory can produce in t hours per day is The total cost of operating the factory for t hours is given by (a) The average cost per item produced is given by Write a formula for the average cost per item. (b) Use this function to complete the following table.

16. The number of items that a factory can produce in t hours per day is The total cost of operating the factory for t hours is given by (c) Describe what happens to the average cost when the number of hours the factory operates is reduced to almost 1 hour. (d) Describe what happens to the average cost when the number of hours the factory operates is increased to almost 24 hours.