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6.4 & 6.5 Adding & Subtracting Rational Expressions. Finding Least Common Denominators: Monomials. Find the LCD of the numbers List any variable that occurs ANYWHERE in ANY denominator Give each variable its BIGGEST exponent. 3x 2 2x 5. 6. x x. 6.

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## 6.4 & 6.5 Adding & Subtracting Rational Expressions

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**Finding Least Common Denominators: Monomials**• Find the LCD of the numbers • List any variable that occurs ANYWHERE in ANY denominator • Give each variable its BIGGEST exponent 3x2 2x5 6 x x 6 5 5**4a2b 10ab3**20 20 a b a b 2 3 2 3**Making Equivalent Expressions**2 5 • Rewrite numerators • Make new denominators using LCD • Determine: old denom. X ? = LCD and multiply numerator by ? • Write new expressions 3x2 2x5 2 5 (2x3) (3) 6x5 6x5 4x3 15 6x5 6x5**5 3**4a2b 10ab3 5 3 (5b2) (2a) 20a2b3 20a2b3 25b2 6a 20a2b3 20a2b3**The Whole Process**2 5 • Rewrite numerators • Make new denominators using LCD • Make equivalent expressions • Combine Expressions over One Denominator + 3x2 2x5 2 5 (2x3) (3) + 6x5 6x5 4x315 6x5 6x5 + 4x3 + 15 6x5**5 3**- 4a2b 10ab3 5 3 (5b2) (2a) - 20a2b3 20a2b3 25b2 6a - 20a2b3 20a2b3 25b2 – 6a 20a2b3**5**2c 1 6c + (3) 5 + 1 6c 6c 16 6c 8 3c**Polynomial Problems**3 _ 1 x2 – 4 x + 2 3 _ 1 • Factor all polynomials • LCD is all the different “numbers” present (x + 2)(x – 2) (x + 2) 3 _ 1 (x – 2) (x + 2)(x – 2) (x + 2)(x – 2) 3 – 1(x – 2) (x + 2)(x – 2) -x + 5 (x + 2)(x – 2)**4 _ 5**3 x 4 _ 5 x (3) 3x 3x 4x _ 15 3x 3x 4x – 15 3x**x + 2 4**x – 3 + (x + 2) 4 (x – 3) + x – 3 x – 3 x2 – x – 6 4 + x – 3 x – 3 x2 – x – 2 x – 3 (x + 1)(x – 2) x – 3**3 2**+ a2 – 36 6 – a 3 2 + (a + 6)(a – 6) – 1(a – 6) 3 _ 2 (a + 6) (a + 6)(a – 6) (a + 6)(a – 6) 3 – 2a – 12 (a + 6)(a – 6) - 2a - 9 (a + 6)(a – 6)**3x _ 5x x**9x + 2 2 – 9x 81x2 – 4 + 3x 5x x _ + 9x + 2 -1(9x – 2) (9x + 2)(9x – 2) (9x – 2) (9x + 2) 3x 5x x + + (9x + 2)(9x – 2) (9x + 2)(9x – 2) (9x + 2)(9x – 2) 27x2 – 6x + 45x2 + 10x + x (9x + 2)(9x – 2) 72x2 + 5x (9x + 2)(9x – 2)

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