Review Rewriting and Simplifying Fractions Simplifying Rational Expressions

Review: Rewriting and Simplifying Fractions

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

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

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.

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

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