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Simplifying Rational Expressions

Simplifying Rational Expressions. What is Rational Expression?. 15. 25. 5. 1. 5. 4. –. 12. 35. 24. 8. 7. 3. Warm-up. I. Reduce the following fractions in it ’ s SIMPLEST FORM. II. Factor each of the following quadratics. 1. x 2 + 7 x + 12. 1. =. (x + 3 ) ( x + 4 ).

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Simplifying Rational Expressions

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  1. Simplifying Rational Expressions • What is Rational Expression?

  2. 15 25 5 1 5 4 – 12 35 24 8 7 3 Warm-up I. Reduce the following fractions in it’s SIMPLEST FORM II. Factor each of the following quadratics 1. x2 + 7x + 12 1. = (x + 3) ( x + 4) 2. x2 + 21x + 20 2. – = (x + 20) ( x + 1) 3. x2- 6x + 8 3. = (x - 4) ( x - 2)

  3. 2 x (x+2) = x Simplifying Rational Expressions Example 1: (Using GCF) GCF = 2 2 (x +2) (2x +4) = x (x+2)

  4. 3 5 (y–5) = 5 Simplifying Rational Expressions Example 2: (Using GCF) 3 (y–5) 3 (y –5) = (5y –25) GCF = 5

  5. 9 3 5 (y + 7) x (x+2) = = 5 x Simplifying Rational Expressions Your Turn! (Using GCF) 9 (y+7) 9 (y + 7) 1. = (5y+35) GCF = 5 GCF = 3 3 (x +2) (3x + 6) 2. = 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. 5 (x–5) 5 = (x-2) Simplifying by factoring Your Turn! “big x method” 5 (x–5) = (x - 2)(x – 5) x2 - 7x + 10 Factor

  8. = 3 x3 6 5xxx 6y2 2yyyy 25xx 2. = = = = y2 5 25 2yy 2y4 Simplifying by cancelations Example 1: Cancelations 5x5 5xxxxx 1. = 25x2 5 3 6yy

  9. Simplifying Rational Expressions At the end of the period, you should be able to: • More on Simplifying Rational Expressions 1. Simplify Rational expressions 2. Finding factors of quadratic equations

  10. x3 (x+8) 6 = = = 3y2 x 5 Warm-up Simplify the following RATIONAL EXPRESSIONS 6 (y+2) 1. (5y+10) x2 + 12x + 32 2. x (x+4) 3x5y2 3. 2. 9x2y4

  11. (x-6) (x+2) (x+3) (x+4) Your Turn 1 (x+4) (x-6) (x-3) (x+2) (x+5) (x+3) = = = = x2 - 4x - 12 (x+5) (x-3) x2 - x - 6 Simplifying Rational Expressions Example 1 x2 + 7x + 12 x2 + 8x + 15

  12. 7x (x - 5) 4x (x+2) Your Turn 7 4 3x (x - 5) 3x (x+2) = = = = 7x2– 35x 3 3 3x2 – 15x Simplifying Rational Expressions Example 2 GCF = 4x 4x2 + 8x 3x2 + 6x GCF = 3x GCF = 7x GCF = 3x

  13. Your Turn! 12x2 4x2 6x 12x2 2x ( 2x – 3 ) 3 ( x+2 ) = = = = 2x - 3 12x2 x+2 (4x2 – 6x ) Simplifying Rational Expressions Example 3 4 12x2 3x + 6 ( 3x + 6 ) GCF = 3 x 6 GCF = 2x

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