1. Multiplying and Dividing Rational Expressions
Section 8.2 in Textbook

2. Rational Expression – a quotient of two polynomials Examples: or or
Simplify rational expressions in the same way as you simplify fractions.
Divide out common factors in the numerator and denominator

3. Simplifying Rational Expressions
You will be asked to simplify expressions and then determine values for which the expression would be undefined…
Undefined expressions – when the denominator of an expression equals ZERO!?!
Must use ORIGINAL denominator (not reduced form) to find these answers.

4. Examples:
Simplify. Identify any x-values for which the expression is undefined. (Use original denominator!!) A. B. C.

5. Multiplying Rational Expressions
Factor all the numerators and denominators completely.
Divide out common factors of numerators and denominators.
Multiply numerators. Then multiply denominators.
Be sure the numerator and denominator have no common factors other than 1.

6. Examples: D. E.

7. Examples: F. G.

8. Dividing Rational Expressions
To divide fractions, you must …
Multiply by its reciprocal??
Keep, change, flip??
Keep the first fraction
Change the sign to multiply
Flip the second fraction
Apply multiplication rules after the problem has been set up!!

9. Examples: H. J.

10. Examples: K.

11. Your Turn
Simplify. Identify any x-values for which the expression is undefined Multiply or Divide. Assume all expressions are defined

12. Solving Simple Rational Equations
Simplify the numerator and denominator - factor out any common terms
Solve for x…
Make sure to look for excluded values – they can lead to a NO SOLUTION!?!

13. Examples:
M. N.
P. Q.