(b-c)/c can be separated into b/c-c/c, which is the same as b/c - 1.
so
a= b/c -1
add one to both sides of equations
a+1 = b/c -1+1
1 cancels out on the right side leaving
a+1 = b/c
multiply both sides by c
c ×(a+1)= (b/c)×c
c cancels out on the right side making
c×(a+1) = b
divide both sides by a+1
c =b/(a+1)
