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?