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9.5 Adding and Subtracting Rational Expressions

9.5 Adding and Subtracting Rational Expressions. 5/3/2013. 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. a. . b. . –. +. 2 x. 2 x. x. x. 3. 3. +. +. 3. 5. 8.

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9.5 Adding and Subtracting Rational Expressions

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  1. 9.5 Adding and Subtracting Rational Expressions 5/3/2013

  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 2 x a. b. – + 2x 2x x x 3 3 + + 3 5 8 4 3 5 + a. = = = + Add numerators and simplify. 2x 2x 2x x 2x x 2 – x 2 b. – Subtract numerators. = x 3 x 3 + + x 3 + Add and Subtract with Like Denominators Perform the indicated operation.

  4. 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.

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

  6. Example 2 1 1 1 1 , a. b. 6x 8x3 2x 4 3x 9 – + Find the LCD of Rational Expressions Find the least common denominator. , a. 6x = 2 •3•x 8x3 =2•2•2•x•x•x LCD:2•2•2•3•x•x•x = 24x3 b. 2x - 4 = 2(x – 2) 3x + 9 = 3(x + 3) LCD: 2•3 (x-2)(x+3) = 6(x-2)(x+3)

  7. 2 1 , 4. 9x2 ANSWER 3x 9x2 3 x , ( ( x2 x2 5. ANSWER – + ( ( x 2 x2 4 – – x x1 – , ( ( 6. x1 2x 1 ANSWER ( ( + + 2x 1 x1 + + Find the LCD of Rational Expressions Checkpoint Find the least common denominator.

  8. LCD: 4•3 = 12 Basic Example of Adding Fractions with different denominators.

  9. Perform the indicated operation. 3 4 2x 3 b. a. + + 2x x2 – x 2 x 5 + Example 3 Add with Unlike Denominators Find LCD: Find LCD:

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

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

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

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

  14. Example 4 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 .

  15. Example 4 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. – =

  16. ANSWER x 2 1 1 – – 9. – x2 1 x 1 x 1 ( ) ( ) – – + x 1 + Add and Subtract with Unlike Denominators Checkpoint Perform the indicated operation.

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