1. Rewriting Fractions: Factoring, Rationalizing, Embedded

2. Simplifying Rational Expressions Simplify: Can NOT cancel since everything does not have a common factor and its not in factored form CAN cancel since the top and bottom have a common factor Factor Completely This form is more convenient in order to find the domain

3. Polynomial Division: Area Method Simplify: x 4 +0x 3 –10x 2 +2x + 3 x - 3 x 3 x 4 -3x 3 3x33x3 3x23x2 -9x 2 -x2-x2 -x-x 3x3x -x-x 3 x 3 + 3x 2 – x – 1 Divisor Dividend (make sure to include all powers of x) The sum of these boxes must be the dividend Needed Check Quotient

4. Rationalizing Irrational and Complex Denominators The denominator of a fraction typically can not contain an imaginary number or any other radical. To rationalize the denominator (rewriting a fraction so the bottom is a rational number) multiply by the conjugate of the denominator. Ex: Rationalize the denominator of each fraction. b. a.

5. Simplifying Complex Fractions Simplify: It is not simplified since it has embedded fractions To eliminate the denominators of the embedded fractions, multiply by a common denominator Check to see if it can be simplified more: No Common Factor. Not everything can be simplified!

6. Trigonometric Identities Simplify: Split the fraction Write as simple as possible Use Trigonometric Identities