A = (B - C)/ C

Multiply both sides by c

Add b to both side c

Factorize the left side

Then you are almost there:)

Solve for C:
A = (B-C)/C

A = (B-C)/C is equivalent to (B-C)/C = A:
(B-C)/C = A

Multiply both sides by C:
B-C = A C

Subtract B+A C from both sides:
C (-1-A) = -B

Divide both sides by -1-A:
Answer: |C = B/(A+1)