1. Lesson 8-1: Multiplying and Dividing Rational Expressions

2. Rational Expression
Definition: a ratio of two polynomial expressions

3. To Simplify A Rational Expression
1. Make sure both the numerator and denominator are factored completely!!!
2. Look for common factors and cancel
Remember factors are things that are being multiplied you can NEVER cancel things that are being added or subtracted!!!
3. Find out what conditions make the expression undefined and state them.

4. Examples: Simplify and state the values for x that result in the expression being undefined1. 2.

5. Examples Cont… Simplify3. 4.

6. Operations with Rational Expressions
To Multiply Rational Expressions:
Factor and cancel where possible. Then multiply numerators and denominators
Define x-values for which the expression is undefined
To Divide Rational Expressions:
Rewrite the problem as a multiplication problem with the first expression times the reciprocal of the second expression. Then factor and cancel where possible. Multiply numerators and denominators

7. Examples: Simplify 5. 6. 7.

8. Polynomials in Numerator and Denominator
Rules are the same as before…
1. Make sure everything is factored completely
2. Cancel common factors
3. Simplify and define x values for which the expression is undefined.

9. Examples: Simplify and define x values for which it is undefined8. 9.

10. Examples:
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11. Simplifying complex fractions
A complex fraction is a rational expression whose numerator and/or denominator contains a rational expression

12. To simplify complex fractions
Same rules as before
Rewrite as multiplication with the reciprocal
Factor and cancel what you can
Simplify everything
Multiply to finish

13. Examples:
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