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what is the quotient in simplified form? State any restrictions on the variable. (6-x)/x^2+3x-28 divided x^2-36/x^2+5x-36

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2 answers

  1. {(6-x)/[(x+7)(x-4)]} / {[(x+6)(x-6)]/[(x+9)(x-4)]} = [(6-x)(x+9)(x-4)] / [(x+7)(x-4)(x+6)(x-6)] =

    -(x+9) / [(x+7)(x+6)]

    x cannot equal -6 or -7 ... division by zero is a no-no

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  2. (6-x)/(x^2+3x-28) ÷ ( (x^2-36)/(x^2+5x-36) )
    = (6-x)/(x^2+3x-28) * (x^2+5x-36)/(x^2 - 36)
    = (6-x)/( (x+7)(x-4) ) * (x+9)(x-4)/((x-6)(x+6) )
    = -(x+9)/( (x+7)(x+6) ) , x ≠ 4,6

    The restriction of x ≠ 4,6 must be stated, otherwise we actually did divide by zero.
    The restriction of x ≠ -7, -6 is implied, in the original problem as well as the answer, it doesn't really have to be stated

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