P6 Rational Expressions

Warm-up Simplify the following:

Rational expression Activity: Graph the expression above in your calculator. And fill in the table: Do you notice anything unusual? Discuss possible reasons for your result with your neighbor. XY

Example 1: Excluding Numbers from the Domain

Example 2: Simplifying Rational Expressions

Example 3: Multiplying Rational Expressions

Example 4: Dividing Rational Expressions

Text Example Find all the numbers that must be excluded from the domain of each rational expression. This denominator would equal zero if x = 2. This denominator would equal zero if x = -1. This denominator would equal zero if x = 1. SolutionTo determine the numbers that must be excluded from each domain, examine the denominators.

Simplifying Rational Expressions 1. Factor the numerator and denominator completely. 2. Divide both the numerator and denominator by the common factors.

Example Simplify: Solution:

Multiplying Rational Expressions 1. Factoring all numerators and denominators completely. 2. Dividing both the numerator and denominator by common factors. 3. Multiply the remaining factors in the numerator and multiply the remaining factors in the denominator.

Example Multiply and simplify: Solution:

Example Divide and simplify: Solution:

Example Add: Solution:

Finding the Least Common Denominator 1. Factor each denominator completely. 2. List the factors of the first denominator. 3. Add to the list in step 2 any factors of the second denominator that do not appear in the list. 4. Form the product of each different factor from the list in step 3. This product is the least common denominator.

Adding and Subtracting Rational Expressions That Have Different Denominators with Shared Factors 1. Find the least common denominator. 2. Write all rational expressions in terms of the least common denominator. To do so, multiply both the numerator and the denominator of each rational expression by any factor(s) needed to convert the denominator into the least common denominator. 3. Add or subtract the numerators, placing the resulting expression over the least common denominator. 4. If necessary, simplify the resulting rational expression.

Example Subtract: Solution:

Rational Expressions