Algebra

Multiply through by (x-c) to get

a (x-c)/(x-a) = c-b       now multiply by x-a

a (x-c) = (c-b)(x-a)      expand both sides

ax   - ac    =  cx - ac - bx + ba       add ac to both sides

ax = cx - bx + ba          put all of the x factors on the left

ax + bx - cx = ba          factor out x on the left

x ( a+ b -c) = ba          divide bt (a+b-c)

x = ba / (a+b-c)                   Just check my math a bit, but that is how to do it......