The solution for a being rational is quite same as your previous problem. You are dividing the piece in the ratio x:y (g.c.d(x,y)=1) If it can be divided into two equal parts then sum(x^i y^j / (x+y)^i+j)=.5 If you add the fractions taking the l.c.m of the denominators then in the numerator you will find some terms relating to x,y,x+y It is easy to prove that no two terms in the numerator will have same power of x+y. Take the second least power of x+y in the numerator. It should divide all the terms in the numerator. But easy to see that it cannot divide the term with least power of x+y unless it divides 2, but this is impossible since a is not equal to 1