Simplify Multiply and Divide Rational Expressions 12142021 9

Simplify, Multiply and Divide Rational Expressions 12/14/2021 9: 11 AM 1

Example 1 Simplify

Example 2 Simplify 2 1 Subtract exponents variable stays where largest exponent is

Example 3 Simplify 8 5

– Restrictions: Any value that makes the rational expression undefined (results in a zero in the denominator) • Factor the expression • Solve the factors (before cancelling) by setting them equal to zero • The results are the restrictions 12/14/2021 9: 11 AM 5

Example 4 Simplify Identify any x-values for which the expression is undefined. 12/14/2021 9: 11 AM 6

Example 6 Simplify Identify any x-values for which the expression is undefined. If it is not in the order you usually see…switch it!! Factor out – 1 in the numerator so that x 2 is positive, and reorder the terms. 12/14/2021 9: 11 AM 7

Example 7 Simplify Do NOT Cancel the “x” or the “ 3”!!!!! 12/14/2021 9: 11 AM 8

Rules of Multiplying Expressions 1. Factor numberator(s) and denominator(s) 2. Extend the fraction bar 3. Cancel [top/bottom] out the factors if needed and simplify. 12/14/2021 9: 11 AM 9

Rules of Divide Expressions 1. KFC!!! Keep it (the first fraction), Flip it (the second fraction), Change it (the sign – division becomes multiplication) 2. Multiply and simplify! 12/14/2021 9: 11 AM 10

Example 9 Simplify 12/14/2021 9: 11 AM 11

Example 10 12/14/2021 9: 11 AM 12

Example 11 Simplify 12/14/2021 9: 11 AM 13

Example 12 Simplify 12/14/2021 9: 11 AM 14