A/BC + D/EF + G/HI = 1

Each of three fractions has a one-digit numerator and a two-digit denominator. The three fractions together add up to one. Place the nine digits 1-9 into the fractions to make the equation correct.

But since the letters represent digits and not just integers, the already hard equation would be MUCH harder to solve.

Here goes:

A(10E+F)(10H+I) + D(10B+C)(10H+I) + G(10B+C)(10E+F) = (10B+C)(10E+F)(10H+I)

Or...

100AEH + 10AEI + 10AFH + AFI + 100DBH + 10DBI + 10DCH + DCI + 100BGE + 10BGF + 10CEG + CFG = 1000BEH + 100BEI + 100BFH + 10BFI + 100CEH + 10CEI + 10CFH + CFI

And that's just a nightmare.