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)

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)