algebra

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(6x-2y)/(x^2+xy-2y^2)-(3x+2y)/(x^2+3xy-4y^2)

  • algebra -

    x^2+xy-2y^2 = (x+2y)(x-y)
    x^2+3xy-4y^2 = (x+4y)(x-y)

    so, the LCD = (x+2y)(x+4y)(x-y) and putting it all over that LCD, the numerator then becomes

    (6x-2y)(x+4y) - (3x+2y)(x+2y)
    = 6x^2 +22xy - 8y^2
    - 3x^2 +8xy + 4y^2

    = 3x^2 + 14xy - 12y^2

    so, the final fraction is

    3x^2 + 14xy - 12y^2
    -------------------------
    (x+2y)(x+4y)(x-y)

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