algebra

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6x^2+13x+6/3x^2+x-2=

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  1. (6X^2 + 13X + 6) / (3X^2 + X - 2) =
    Factor numerator and denominator and get:
    (3X+2)(2X+3) / (3X-2)(X+1).

    The AC method was used for factoring:
    6X^2 + 13X + 6.

    A*C = 6*6 = 36 = 1*36 = 2*18 = 4*9.
    Select the pair whose sum equals B(13).
    6X^2 + 4X+9X + 6,
    Group the 4 terms in factorable pairs:
    (6X^2 + 4X) + (9X + 6) =
    Factor each binomial:
    2X(3X + 2) + 3(3X + 2)=
    (3X + 2)(2X + 3).

    Repeat the procedure for the denominator.

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