Quiz 8-3 m < n : y = 0 m = n : y = 1. x-intercepts: (zeroes of numerator) 2. vertical asymptotes: zeroes of denominator 3. horizontal asymptotes: 4. End.

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Presentation transcript:

Quiz 8-3 m < n : y = 0 m = n : y = 1. x-intercepts: (zeroes of numerator) 2. vertical asymptotes: zeroes of denominator 3. horizontal asymptotes: 4. End behavior: y = Find:

8-4: Multiplying and Dividing Rational Expression.

Simplifying Rational expressions Expand the numerator and denominators into products of separate fractions. into products of separate fractions. Now simplify = 2 * 1 * y = 2y

Your Turn: Simplify:1. 2.

Another example Simplify: Expand the numerator and denominators into products of separate fractions. into products of separate fractions.

Your Turn: 3. 4.

Another Example Look for common factors in numerator and denominator in numerator and denominator

Your Turn: 5. Simplify (hint: look for common factors)

Multiply then simplify Yuck!

BE CAREFUL!!!!! Addition and Subtraction mean: Combine the terms into one term (if you can) No, no, no, no, no!!! If you can’t (unlike terms) they still are connected to each other. Put it into a parentheses.

Multiplying Rational Expressions Do you multiply first or do you simplify THEN multiply? Your turn: 6. Simplify the above factored rational expression.

Divide Rational Expressions I don’t know how to divide fractions. divide fractions. What do I do? Multiply by the reciprocal Can this fraction be reduced?

Dividing Rational Expressions Multiply then simplify OR simplify then multiply?