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Simplifying Rational Expressions

Simplifying Rational Expressions. At the end of the period, you should be able to:. 1. Multiply and divide rational expressions. (x-4). (x+4). Your Turn!. (x-2) (x-4). (x+3) (x+4). (x+5) (x+3). (2x+7) (x-2). =. =. =. =. (x-2) (x-4). (x+5). (2x+7). x. (2x+7) (x-2).

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Simplifying Rational Expressions

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

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

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

  4. 15y (5+x) (6x3) 12x5 10x2 5 x = = 3y2 (5X) (7x+2) 9y4 (5+x) 10x2 Dividing Rational Expressions Example 2 12x5 10x2 ÷ 9y4 (5+x) 15y (5+x) 5 6x3 = 5x 3y2

  5. 2 x (x+2) = x Simplifying Rational Expressions Example 1: (Using GCF) GCF = 2 2 (x +2) (2x +4) = x (x+2)

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

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

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

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

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

  11. 4x (x+2) 4 3x (x+2) = = 3 Simplifying Rational Expressions GCF = 4x 4x2 + 8x 3x2 + 6x GCF = 3x

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