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how would you solve 3/(x+2) - 6/3x = 6/(3x+6) algebraically and graphically?

  • pre-calc -

    First rewrite the left side with a common denominator as:
    [9x - 6(x+2)]/(3x^2+6x)
    = (3x -12)/(3x^2+6x)

    Then multiply the numerator and denominator of the right side by x. That does not change its value but gives you the same denominator on both sides. In that situation the numerators are equal, so
    3x - 12 = 6x
    3x = -12
    x = -4

    Check: -3/2 +6/12 =?= 6/-6 = -1 ok

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