Lesson31 - : 1. Factor each denominator. 2. Find a product...

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1 Lesson 31 Section 6.2 Addition or Subtraction of Rational Expressions Remember: Fractions (rationals) can only be added or subtracted if they have a common denominator. For example: 8 5 8 2 8 3 = + To add or subtract rational expressions with the same denominator : 1. Add or Subtract the numerators. 2. Keep the denominator. 3. Factor, if possible. 4. Simplify, if possible. A B A B C C C ± ± = Examples: 1) = + + + + 7 8 7 2 6 x x x 2) = + a a 3 7 3 5 3) = - - - - + 2 3 2 2 4 y y y y 4) = - - - - - 25 7 4 25 2 3 2 2 a a a a
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2 When denominators are opposites , the denominators can be made the same polynomial by multiplying both numerator and denominator of one rational expression by 1 - . Ex 5) Examine the following. ( ) ( ) 2 2 2 2 2 2 2 2 2 7 1 16 16 7 1 1 16 16 1 1 ( 7) 16 16 ( 7) ( 1) 16 7 1 2 8 16 16 2( 4) 2 ( 4)( 4) 4 x x x x x x x x x x x x x x x x x x x x x x x x - - - = - - - - -  -  - - -  - - - = - - - - - - = - - + - - = = - - - = = + - + + When denominators are unlike, a common denominator must be found and the fractions are rewritten by multiplying numerator and denominator by the same nonzero quantity. To find the least common denominator (LCD)
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Unformatted text preview: : 1. Factor each denominator. 2. Find a product that contains each different factor the greatest number of times it occurs in any denominator . Examples: 6) ) 2 ( , ) 2 ( 2 + + x x x 7) ) 5 )( 1 ( , ) 1 )( 3 (-+ +-x x x x 8) 2 4 3 4 6 54 , 4 12 x x x x-+ 3 8.5) 2 2 2 2 , , 2 ( 2) 4 x x x x x + +-To add or subtract rational expressions with different denominators : 1. Find the LCD as outlined previously. 2. Multiply each numerator by the missing factor needed in order to write with the LCD. 3. Combine numerator terms together over the common denominator. 4. Factor and simplify, if possible. Examples: 9) = +-+-+ 4 2 1 3 a a a a 10) =-+ + 5 2 3 x x 11) =--+ +-+ 8 2 3 2 9 4 3 7 2 2 y y y y y 4 12) =-+--y x y x y x xy 2 2 6 13) = + +-+ + 20 9 5 30 11 2 2 x x x x x 14) =-+ +-+ +-4 3 2 5 2 2 2 a a a a...
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Lesson31 - : 1. Factor each denominator. 2. Find a product...

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