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Unit: Rational Functions Chapter 9-5: Adding and Subtracting Rational Expressions

Unit: Rational Functions Chapter 9-5: Adding and Subtracting Rational Expressions. Essential Question: How do you add and subtract two rational expressions?. Chapter 9-5: Adding and Subtracting Rational Expressions.

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Unit: Rational Functions Chapter 9-5: Adding and Subtracting Rational Expressions

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  1. Unit: Rational FunctionsChapter 9-5: Adding and Subtracting Rational Expressions Essential Question: How do you add and subtract two rational expressions?

  2. Chapter 9-5: Adding and Subtracting Rational Expressions • Just like with fractions, terms need to have a common denominator in order for their numerators to be added or subtracted together. • After they’re added/subtracted, fractions can be simplified. • Sometimes, you will need to find the least common denominator (LCD). To do this, you find the least common multiple of the denominators.

  3. Chapter 9-5: Adding and Subtracting Rational Expressions • To find the least common multiple • Find the prime factors of each expression • Write each prime factor the greatest number of times it appears in either expression • Simplify where possible • Find the LCM of 4x2 – 36 and 6x2 + 36x + 54 • Step 1 • 4x2 – 36 • 6x2 + 36x + 54 • Step 2 • Step 3 = 4(x2 – 9) = (2)(2) (x + 3) (x – 3) (x + 3)(x + 3) = 6(x2 + 6x + 9) = (2) (3) • (3) appears once, • (2) appears twice, • (x – 3) appears once, • (x + 3) appears twice • (2)(2)(3)(x – 3)(x + 3)(x + 3) = 12(x – 3)(x + 3)2

  4. Chapter 9-5: Adding and Subtracting Rational Expressions • Your Turn #1 • Find the LCM of 3x2 – 9x - 30 and 6x + 30 • Step 1 • 3x2 – 9x – 30 • 6x + 30 • Step 2 • Step 3 = 3(x2 – 3x – 10) (x – 5) = (3) (x + 2) = 6(x + 5) = (2) (3) (x + 5) • (3) appears once, • (2) appears once, • (x + 5) appears once, • (x - 5) appears once, • (x + 2) appears once • (2)(3)(x – 5)(x + 5)(x + 2) = 6(x – 5)(x + 5)(x + 2)

  5. Chapter 9-5: Adding and Subtracting Rational Expressions • Your Turn #2 • Find the LCM of 5x2 + 15x + 10 and 2x2 – 8 • Step 1 • 5x2 + 15x + 10 • 2x2 – 8 • Step 2 • Step 3 = 5(x2 + 3x + 2) (x + 2) = (5) (x + 1) (x – 2) = 2(x2 – 4) = (2) (x + 2) • (5) appears once, • (2) appears once, • (x + 1) appears once, • (x + 2) appears once, • (x – 2) appears once • (2)(5)(x + 2)(x + 1)(x – 2) = 10(x + 2)(x + 1)(x – 2)

  6. Chapter 9-5: Adding and Subtracting Rational Expressions • Now that we understand how to find the least common multiple (which is also our least common denominator), let’s use that to add/subtract fractions • We multiply each term in the problem by what is missing from the LCD

  7. Chapter 9-5: Adding and Subtracting Rational Expressions • Simplify • Find the LCM • (x + 4)(x + 1) with (3)(x + 1) = (3)(x + 4)(x + 1) • Multiply left side (top and bottom) by (3) • Multiply right side (top and bottom) by (x + 4)

  8. Chapter 9-5: Adding and Subtracting Rational Expressions • Simplify • Find the LCM • Multiply left side (top and bottom) by • Multiply right side (top and bottom) by • (x – 6)(x + 2) with (2)(2)(x + 2) = (4)(x – 6)(x + 2) • (4) • (x - 6)

  9. Chapter 9-5: Adding and Subtracting Rational Expressions • Simplify • Find the LCM • Multiply left side (top and bottom) by • Multiply right side (top and bottom) by • 5(y + 5)(y – 5) with (3)(y + 5) = (3)(5)(y + 5)(y – 5) • (3) • 5(y - 5)

  10. Chapter 9-5: Adding and Subtracting Rational Expressions • Page 517 – 518 • Problems 5 – 21 (odd) • Show your work!!!

  11. Unit: Rational FunctionsChapter 9-5: Adding and Subtracting Rational ExpressionsDay 3 Essential Question: How do you add and subtract two rational expressions?

  12. Chapter 9-5: Adding and Subtracting Rational Expressions • A complex fraction is a fraction that has a fraction in its numerator, denominator, or both. A few examples: • To simplify a complex fraction, multiply all terms by the LCD of all embedded fractions

  13. Chapter 9-5: Adding and Subtracting Rational Expressions • Simplify • This function has two embedded denominators, x and y, so the LCD of all embedded denominators is xy. • Multiply all terms by xy.

  14. Chapter 9-5: Adding and Subtracting Rational Expressions • Simplify • Multiply all terms by: x

  15. Chapter 9-5: Adding and Subtracting Rational Expressions • Simplify • Multiply all terms by: 2y

  16. Chapter 9-5: Adding and Subtracting Rational Expressions • Simplify • Multiply all terms by: x(x + 1)(x – 1)

  17. Chapter 9-5: Adding and Subtracting Rational Expressions • Page 517 – 518 • Problems 22 – 30 (all) • Show your work!!!

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