Squaring (i) and subtracting (ii) from the result, we get:
2(A*B+B*C+C*A) =1, so that: A*B+B*C+C*A =1/2.
Accordingly, A, B and C are roots of the equation:
x^{3} - 2x^{2}+x/2 - 4= 0 .....(iv)

Now, A*B + C – 1 = 4/C+C-1, and so:
(A*B + C - l)^{-1} = (4/C+C-1)^{-1} = C/(C^{2} - C +4) .....(v)
Similarly, (B*C + A - l)^{-1} = (4/A+A-1)^{-1} = A/(A^{2} - A +4) ...(vi)
(C*A + B - l)-1 = (4/B+B-1)^{-1} = B/(B^{2} - B +4) ...(vii)

From (iv): C^{3} - 2C^{2}+C/2 - 4= 0
or, (C^{2} - C +4)(C-1) = 9C/2
or, C/(C^{2} - C +4) = 2(C-1)/9
Similarly, A/(A^{2} - A +4) = 2(A-1)/9
and, B/(B^{2} - B+4) = 2(B-1)/9