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)