Lesson 8-1: Multiplying and Dividing Rational Expressions

Rational Expression Definition: a ratio of two polynomial expressions

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.

Examples: Simplify and state the values for x that result in the expression being undefined 1. 2.

Examples Cont… Simplify 3. 4.

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

Examples: Simplify 5. 6. 7.

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.

Examples: Simplify and define x values for which it is undefined 8. 9.

Examples: 10. 11.

Simplifying complex fractions A complex fraction is a rational expression whose numerator and/or denominator contains a rational expression

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

Examples: 12. 13.