Simplifying Rational Expressions

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Presentation transcript:

Simplifying Rational Expressions At the end of the period, you should be able to: 1. Multiply and divide rational expressions

Multiplying Rational Expressions Example 1 (x+3) (x+4) = (x+4) (x+5) = (x+3) (x+4) x (x+5) (x+3) (x+5) (x+3) Your Turn! x (x-2) (x-4) (2x+7) (x-2) = (x-4) (2x+7) = (x-2) (x-4) (2x+7) (x-2)

Dividing Rational Expressions Example 3 2x 7x+2 ÷ 3 (5+x) 15x (5+x) 5 2x 3 (5+x) x 7x+2 15x (5+x) 15x (5+x) (2x) 3 (5+x) (7x+2) = 5x (2x) (7x+2) = = 10x2 (7x+2)

Dividing Rational Expressions Example 2 12x5 10x2 ÷ 9y4 (5+x) 15y (5+x) 5 6x3 = 5 (6x3) 3y2 (5X) = 10x2 (7x+2) 12x5 9y4 (5+x) x 10x2 15y (5+x) = 5x 3y2

Simplifying Rational Expressions Example 1: (Using GCF) GCF = 2 (2x +4) 2 (x +2) = 2 x = x (x+2) x (x+2)

Simplifying by factoring Example 1: “big x method” Factor = (x+3) 2 x2 + 7x + 12 (x + 4)(x + 3) = 2 (x+4) 2 (x+4)

Simplifying by cancelations Example 1: Cancelations 5x5 5xxxxx 5xxx 25 = x3 5 = 1. = 25xx 25x2 5

Simplifying Rational Expressions x2 + 7x + 12 = (x+3) (x+4) = (x+4) (x+5) (x+5) (x+3) x2 + 8x + 15

-------------------------------------------------------------- GCF = 2 (2x +4) 2 (x +2) = 2 x = x (x+2) x (x+2) -------------------------------------------------------------- (x+3) (x+4) = (x+4) (x+5) = (x+3) (x+4) x (x+5) (x+3) (x+5) (x+3)

Dividing Rational Expressions ÷ 3 (5+x) 15x (5+x) 5 2x 3 (5+x) x 7x+2 15x (5+x) 15x (5+x) (2x) 3 (5+x) (7x+2) = 5x (2x) (7x+2) = = 10x2 (7x+2)

Simplifying Rational Expressions GCF = 4x 4x2 + 8x = 4x (x+2) = 4 3 3x (x+2) 3x2 + 6x GCF = 3x