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Math Help - transformations

  1. #1
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    transformations

    ok im having a bit of trouble with interpreting this question:
    Show that: 3x + 2/x+1 = 3 - (1/x+1)
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  2. #2
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    Quote Originally Posted by RoboStar View Post
    ok im having a bit of trouble with interpreting this question:
    Show that: 3x + 2/x+1 = 3 - (1/x+1)
    You could do \frac{3x+2}{x+1} using polynomial long division.

    Or you could assume that the result will be of the form A + \frac{B}{x+1} and solve for A and B.

    Or you could do some fancy re-arranging:

    \frac{3x+2}{x+1} = 3\, \left(\frac{3x+2}{3(x + 1)}\right)


     = 3\, \left(\frac{3x+2}{3x + 3}\right) = 3\, \left(\frac{(3x+3)-1}{3x + 3}\right)


     = 3\, \left(1 - \frac{1}{3x + 3}\right) = 3 - \frac{1}{x + 1}.
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