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Review: Rewriting and Simplifying Fractions

Review: Rewriting and Simplifying Fractions. Simplifying Rational Expressions. Can NOT cancel since everything does not have a common factor and its not in factored form. Simplify:. Factor Completely. CAN cancel since the top and bottom have a common factor.

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Review: Rewriting and Simplifying Fractions

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  1. Review: Rewriting and Simplifying Fractions

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

  3. Polynomial Division: Area Method Simplify: Quotient x3 3x2 -x -1 Dividend (make sure to include all powers of x) x x4 3x3 -x2 -x The sum of these boxes must be the dividend Divisor - 3 -3x3 -9x2 3x 3 x4 +0x3 –10x2 +2x + 3 Needed Needed Needed Check Needed x3 + 3x2 – x – 1

  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. a. b.

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

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

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