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Section 6.2 Adding & Subtracting Rational Expressions

Section 6.2 Adding & Subtracting Rational Expressions. Adding & Subtracting Rational Expressions with the Same Denominators Finding the LCD of 2 or more Polynomial Denominators Adjusting Opposite Factors in Denominators Adding & Subtracting Rational Expressions

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Section 6.2 Adding & Subtracting Rational Expressions

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  1. Section 6.2 Adding & Subtracting Rational Expressions • Adding & Subtracting Rational Expressions • with the Same Denominators • Finding the LCD of 2 or more Polynomial Denominators • Adjusting Opposite Factors in Denominators • Adding & Subtracting Rational Expressions • with Unlike Denominators • 1 1 ? • ------------- + -------------- = ---------------- 6.2

  2. Adding and Subtracting Fractions with Identical Denominators Perform the operation: 6.2

  3. Finding the LCD (must be done before adding or subtracting 2 or more RE’s) 1.Factor each denominator completely into primes. 2. List all factors of each denominator. (use powers when duplicate factors exist) 3. The LCD is the product of each factor to its highest power. 28z3 = (22) (7)(z3) 3 21z = (3)(7) (z) 4z2 LCD= (22)(3)(7)(z3) Lacks↑ (a2 – 25) = (a + 5)(a – 5) (a + 2) (a + 7a + 10) = (a + 5) (a + 2) (a – 5) LCD = (a + 5)(a – 5)(a + 2) Lacks↑ 6.2

  4. Find the LCD, using a Primes Table • ? ? ?8(x – 3) (x2 – x – 6) (2x2 – 12x + 18) • 8(x – 3) = (2)3(x – 3) (x + 2)(x – 3) • (x2 – x – 6) = (x – 3)(x + 2) 8(x – 3) • (2x2 – 12x + 18) = (2) (x – 3)2 4(x + 2) • LCD = (2)3 (x – 3)2(x + 2) Lacks↑ 6.2

  5. Adjusting an Opposite Denominator • Situation: one factor is the opposite of the other • For 7 and 2 find the LCD3(a – 2) (2 – a) • For the second expression, multiply top and bottom by -1 (doesn’t change its value) • Now 7 and -2 find the LCD3(a – 2) (a – 2) • Do this after factoring, before writing the LCD 6.2

  6. Adding or subtracting rational expressions with unlikedenominators – note any exclusions 1. Find the LCD. 2. Express each rational expression with a denominator that is the LCD. 3. Add (or subtract) the resulting rational expressions. 4. Simplify the result if possible. Exclusions: a ≠ ±2 6.2

  7. Add & Subtract Practice - monomials Exclusions: x ≠ 0 6.2

  8. Add & Subtract Practice - simplifying 6.2

  9. Add & Subtract Practice – change both Exclusions: y ≠ ±1, 6 6.2

  10. Brain Break: 6.2

  11. Add & Subtract – opposite monomials Exclusions: a ≠ 0 6.2

  12. Add & Subtract – opposite binomials + 6.2

  13. Add & Subtract – function simplification Exclusions: x ≠ ±2 6.2

  14. What Next? • 6.3 Complex Fractionsnext time 6.2

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