Simplifying rational expressions

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Presentation transcript:

Simplifying rational expressions

Simplest Form A rational expression is in SIMPLEST FORM when its numerator and denominator are polynomials that have no common factors. *Note: when simplifying we still need to remember holes.

Examples Simplify the expression. State holes, vertical asymptotes, horizontal asymptotes, domain and range. 1.

Examples Simplify the expression. State holes, vertical asymptotes, horizontal asymptotes, domain and range. 2.

Examples Simplify the expression. State holes, vertical asymptotes, horizontal asymptotes, domain and range. 3.

Examples Simplify the expression. State holes, vertical asymptotes, horizontal asymptotes, domain and range. 4.

Multiplying AND DIVIDING RATIONAL EXPRESSIONS

Review: Multiplying fractions

Multiplying Rational Functions You multiply rational functions like you do every other fraction: STRAIGHT ACROSS Steps: Factor where needed Multiply straight across Simplify (Don’t forget to write down your holes before you cancel out common factors)

Multiplying Rational Expressions

Multiplying Rational Expressions

Dividing Rational Expressions Remember: Dividing by a fraction is the same thing as multiplying by the reciprocal. Flip the second fraction, multiply, then simplify. Keep  Change  Flip

Dividing Rational Expressions

Dividing Rational Expressions

Dividing Rational Expressions