T/a + (t-d)/b = 1 Solve for t?

Factor out t then divide by its coefficient
  t/a + (t-d)/b = 1
  t/a + t/b - d/b = 1
  t(1/a+1/b) = 1+d/b
  t = (1+d/b)/(1/a+1/b)
This can be simplified a bit
  t = ((b+d)/b)/((a+b)/(ab))
  t = a(b+d)/(a+b)