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Math Help - difficult algebra problem

  1. #1
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    difficult algebra problem

    If (a^2) + bc = 1 (a, b, c are given real numbers) , show that

    (cx - y(1+a))/(by - x(1-a)) = -(1+a)/b = -c/(1-a).
    where (x and y are any real numbers)

    I thought factoring: bc = 1 - (a^2) = (a+1)(a-1).

    From this it is easily shown that -(1+a)/b = -c/(1-a).

    But how to show that any of these equals: (cx - y(1+a))/(by - x(1-a)).

    It all seems quite intriguing to me. Does anyone see any light here?
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  2. #2
    Moo
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    Hello,

    Factorize above by 1+a and below by b.

    = \frac{1+a}{b} ( \frac{\frac{c}{1+a} x - y}{y-\frac{1-a}{b} x} )

    As you have noticed, bc=(1+a)(1-a)

    Hence \frac{c}{1+a}=\frac{1-a}{b}

    -> = \frac{1+a}{b} ( \frac{\frac{1-a}{b} x - y}{y-\frac{1-a}{b} x} ) = - \frac{1+a}{b}

    Is it clear ? :-)
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  3. #3
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    Thanks moo,
    All clear.
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