Solve the equation
ax + bx = 1
where 0 < a, b < 1 and a + b < 1, in the special cases:
(i) a = b    (ii) a = 1/2,  b=1/4    (iii)a = 1/2,  b=1/3 .

Although you can find exact solutions in special cases like (i) and (ii) it soon becomes apparent that generally you will need to use a numerical method for finding approximate solutions.