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9.5 Adding and Subtracting Rational Expressions

9.5 Adding and Subtracting Rational Expressions. 4/23/2014. Same Denominator:. When adding or subtracting fractions with same denominators, add/subtract the numerators and keep the same denominator. Example 1. 3. 5. +. 2 x. 2 x. 3. 5. 8. 3. 5. +. Add numerators and simplify. . =.

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9.5 Adding and Subtracting Rational Expressions

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  1. 9.5 Adding and Subtracting Rational Expressions 4/23/2014

  2. Same Denominator: When adding or subtracting fractions with same denominators, add/subtract the numerators and keep the same denominator

  3. Example 1 3 5 + 2x 2x 3 5 8 3 5 + Add numerators and simplify. = = + 2x 2x 2x 2x Add and Subtract with Like Denominators Perform the indicated operation.

  4. Different Denominators: If the denominators are different, find the least common denominator (LCD).

  5. Example 2 1 1 a. 6x 8x3 Find the LCD of Rational Expressions Find the least common denominator. , List the multiples of the number: 6: 6, 12, 18, 24, 30, 36…. 8: 8, 16, 24, 32… Take the Least Common Multiple (LCM): 24 As for the variable, take the one with highest exponent: LCD:

  6. Example 2 1 1 , b. 2x 4 3x 9 – + Find the LCD of Rational Expressions Find the least common denominator. 2x - 4 = 2(x – 2) 3x + 9 = 3(x + 3) 2: 2, 4, 6, 8… 3: 3, 6, 9, 12… LCD: 6(x-2)(x+3) (Take the LCM and multiply by the rest of their factors)

  7. Example 2 3 x , c. x 2 x2 4 – – Find the LCD of Rational Expressions Find the least common denominator. Factors LCD:

  8. Example 2 x x1 – , d. 2x 1 x1 + + Find the LCD of Rational Expressions Find the least common denominator. Factors LCD:

  9. 4: 4, 8, 12, 16.. 3: 3, 6, 9, 12… LCD: 12 Basic Example of Adding Fractions with different denominators. 9 4 13

  10. Perform the indicated operation. 3 4 a. + 2x x2 Example 3 Add with Unlike Denominators Find LCD:

  11. Example 3 Add with Unlike Denominators Find LCD:

  12. Perform the indicated operation. ANSWER 2 3 3x 4 + 7. + x2 2x 2x2 Add and Subtract with Unlike Denominators Checkpoint

  13. ANSWER x2 2x 3 3 x + + 8. + x1 x1 – + x 1 x 1 ( ) ( ) – + Add and Subtract with Unlike Denominators Checkpoint Perform the indicated operation.

  14. Example 4 Add with Unlike Denominators Add: Find LCD:

  15. Homework: 9.5 p.497 #10, 12, 13, 15, 16-24even, 28, 30, 33, 37, 39

  16. Checkpoint 2 4 2 1. ANSWER + – – 3x 3x x x 2 2 x x 2 2. – ANSWER – 1 – x 3 x 3 2x + 3. – ANSWER x 4 x 4 x 4 + + + Add and Subtract with Like Denominators Perform the indicated operation.

  17. Subtracting Polynomials Switch the signs of everything that’s being subtracted and combine like terms. Ex:

  18. Example 1 x 2 – x x 3 3 + + x 2 – x 2 – Subtract numerators. = x 3 x 3 + + x 3 + Subtract with Like Denominators Subtract.

  19. Checkpoint – – x x 2 2 ANSWER x 2 1. – – 1 – x 3 x 3 2x + 2. – x 4 x 4 x 4 + + + Extra Examples

  20. Example 2 1 2 – x2 x 2 x2 4 – – – Subtract with Unlike Denominators Subtract .

  21. ANSWER x 2 1 1 – – – x2 1 x 1 x 1 ( ) ( ) – – + x 1 + Add and Subtract with Unlike Denominators Checkpoint Perform the indicated operation.

  22. Example 2 1 2 – x2 x 2 x2 4 – – – SOLUTION The factors of are and and the factors of are and . So, the LCD is . x2 x 2 x 2 x 1 ( ) ( ) – – – + x2 4 x 2 x 2 ( ) ( ) – – + x 2 x 1 x 2 ( ) ) ( ) ( – + + Subtract with Unlike Denominators Subtract .

  23. Example 2 x x x x x x 2 2 2 2 2 2 ( ( ( ( ( ( ) ) ) ) ) ) + + + + + + x 2 – Subtract numerators. + = 2 x 2 2x 2 – – + Distributive property = x 1 2 Combine like terms. – = – x2 x 2 x2 4 – – – x x x x x 2 2 2 2 2 x x x x x x x 1 1 1 1 1 1 1 ( ( ( ( ( ) ) ) ) ) ( ( ( ( ( ( ( ) ) ) ) ) ) ) – – – – – + + + + + + + 1 2 Factor denominators. – = x 2 x 2 x 1 x 2 ( ) ( ) ( ) ( ) – – + + Subtract with Unlike Denominators 2 Rewrite using LCD. – =

  24. Homework: 9.5 p.497 # 11, 14, 29, 31, 32, 38,40, 41

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