Rewriting Fractions: Factoring, Rationalizing, Embedded.

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Presentation transcript:

Rewriting Fractions: Factoring, Rationalizing, Embedded

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

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

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.

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!

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