严肃讨论。参照埃及分数百度百科的最后面的Pascal代码

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        while (in.hasNextLine()) {
            String[] str = in.nextLine().split("\\/");
            long a = Integer.valueOf(str[0]);
            long b = Integer.valueOf(str[1]);
            long c = 0;
            String res = "";
            for ( ; a != 1 && b % a != 0 ;) {
                c = b / a + 1;
                a = a * c - b;
                b = b * c;
                res += ("1/" + c + "+");
            }
            if (b % a == 0 && a != 1) {
                res += ("1/" + b / a);
            } else if (a == 1) {
                res += ("1/" + b);
            }
            System.out.println(res);
        }
    }
}