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Math

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How do you simplify this?

(x+3/x-6)-2/(x+3/x-6)+8

  • Math - ,

    simplify fractions first:

    (x+3)/(x-6) - 2(x-6)/(x+3) + 8

    now put all over common denominator of (x-6)(x+3)

    (x+3)(x+3) - 2(x-6)(x-6) + 8(x+3)(x-6)
    ---------------------------------------
    (x-6)(x+3)

    = (7x^2+6x-207)//(x^2-3x-18)

  • Math - ,

    The above answer is not really a satisfying "simplification." How about this?

    x+3/x-6 = 1 + 9/(x-6)
    x-6/x+3 = 1 - 9/(x+3)

    so, we have

    1 + 9/(x-6) + 2(1 - 9/(x+3)) + 8
    9/(x-6) - 18/(x+3) + 11

  • Math - ,

    "-" got lost.
    Of course, I meant

    9/(x-6) + 18/(x+3) + 7

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