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Adding and Subtracting Rational Expressions

Learn how to determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and two. Practice simplifying monomial and polynomial denominators. Solve complex fractions with different LCDs.

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Adding and Subtracting Rational Expressions

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  1. LESSON 8–2 Adding and Subtracting Rational Expressions

  2. A. B. C. D. 5-Minute Check 3

  3. Targeted TEKS A2.7(F) Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two. Mathematical Processes A2.1(A), A2.1(B) TEKS

  4. You added and subtracted polynomial expressions. • Determine the LCM of polynomials. • Add and subtract rational expressions. Then/Now

  5. LCM of Monomials and Polynomials B. Find the LCM of x3 – x2– 2x and x2– 4x + 4. x3 – x2– 2x = x(x + 1)(x – 2) Factor the first polynomial. x2 – 4x + 4 = (x – 2)2 Factor the second polynomial. LCM = x(x + 1)(x – 2)2 Use each factor the greatest number of times it appears as a factor. Answer:x(x + 1)(x – 2)2 Example 1B

  6. B. Find the LCM of x3 + 2x2 – 3x and x2 + 6x + 9. A.x(x + 3)2(x – 1) B.x(x + 3)(x – 1) C.x(x – 1) D. (x + 3)(x – 1) Example 1B

  7. Concept

  8. Simplify . Monomial Denominators The LCD is 42a2b2. Simplify each numerator and denominator. Add the numerators. Example 2

  9. Answer: Monomial Denominators Example 2

  10. Simplify . A. B. C. D. Example 2

  11. Simplify . The LCD is 6(x – 5). Polynomial Denominators Factor the denominators. Subtract the numerators. Example 3

  12. Distributive Property Combine like terms. Simplify. Answer: Polynomial Denominators Simplify. Example 3

  13. Simplify . A. B. C. D. Example 3

  14. Simplify . Complex Fractions with Different LCDs The LCD of the numerator is ab. The LCD of the denominator is b. Example 4

  15. Write as a division expression. Complex Fractions with Different LCDs Simplify the numerator and denominator. Multiply by the reciprocal of the divisor. Simplify. Example 4

  16. Answer: Complex Fractions with Different LCDs Example 4

  17. Simplify . A. B. –1 C.D. Example 4

  18. Simplify The LCD of all of the denominators is xy. Multiply by Complex Fractions with Same LCD Distribute xy. Example 5

  19. Complex Fractions with Same LCD Answer: Example 5

  20. Simplify A.B. C.D. Example 5

  21. LESSON 8–2 Adding and Subtracting Rational Expressions

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