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   

You can find exact solutions to the equation ax + bx = 1 in special cases like (i) and (ii).

More generally you will need to use a numerical method for finding approximate solutions. See Equation Attack.