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Math Help - Polynomial Long Division for Rational Functions

  1. #1
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    Polynomial Long Division for Rational Functions

    x^2
    ____
    3x + 1

    How do I simplify this to get the Slant Asymptote?

    I thought that you couldn't divide x^2 by 3x +1 because their degrees don't match.
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  2. #2
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    Oh, wait!

    Is it 1/3x ?
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  3. #3
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    Is what "1/3x"? And do you mean 1/(3x) or (1/3)x?

    To divide x^2 by 3x+1, first write [tex]x^2= x^2+ 0x+ 0.
    How many times does "3x" divide into x^2? (1/3)x times, of course. But you are not done. Now subtract 3x+1 times (1/3)x from x^2: x^2- (1/3)x(3x+1)= x^2- x^2- (1/3)x= -(1/3)x+ 0. How many times does 3x divide into -(1/3)x? -1/9 times. And now you subtract (3x+1) times -1/9 from -(1/3)x+ 0: -(1/3)x- (-1/9)(3x+1)= -(1/3)x+ (1/3)x+ 1/9= 1/9.

    3x+1 divides into x^2 (1/3)x- 1/9 times with remainder 1/9.
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