Fractions with sum 1

Question

Using all numbers 0 to 9 only once, form two fractions whose sum is 1.

I have tried every possible combination but with no luck. I believe the fractions must be xx/xx + xxx/xxx but I am not sure. Any ideas are most welcome. I even tried getting all different ways to select 3 out of 10 digits, then omitting all the primes and trying to make fractions with simple values 1/3, 1/4, 2/5 etc using only different digits but again with no luck! By the way, two years ago I was given a similar one, with three fractions and without the digit 0, for which I found a solution 7/68+9/12+5/34 but now I am stuck!!

Answer 1

$\dfrac{27}{054} + \dfrac{69}{138} = \dfrac{1}{2} + \dfrac{1}{2} = 1$

Or if a leading zero is not allowed.

$\dfrac{135}{270} + \dfrac{48}{96} = \dfrac{1}{2} + \dfrac{1}{2} = 1$

Answer 2

12   609
-- + --- = 1
54   783
-----------
12   748
-- + --- = 1
60   935
-----------
12   357
-- + --- = 1
96   408
-----------
12   735
-- + --- = 1
96   840
-----------
13   485
-- + --- = 1
26   970
-----------
13   678
-- + --- = 1
52   904
-----------
15   486
-- + --- = 1
30   972
-----------
16   485
-- + --- = 1
32   970
-----------
17   504
-- + --- = 1
89   623
-----------
18   276
-- + --- = 1
90   345
-----------
18   372
-- + --- = 1
90   465
-----------
19   308
-- + --- = 1
57   462
-----------
19   273
-- + --- = 1
58   406
-----------
21   375
-- + --- = 1
96   480
-----------
24   507
-- + --- = 1
63   819
-----------
24   531
-- + --- = 1
96   708
-----------
27   309
-- + --- = 1
54   618
-----------
27   306
-- + --- = 1
81   459
-----------
27   630
-- + --- = 1
81   945
-----------
29   307
-- + --- = 1
58   614
-----------
29   310
-- + --- = 1
87   465
-----------
31   485
-- + --- = 1
62   970
-----------
32   169
-- + --- = 1
48   507
-----------
32   417
-- + --- = 1
80   695
-----------
34   269
-- + --- = 1
51   807
-----------
35   148
-- + --- = 1
70   296
-----------
35   481
-- + --- = 1
70   962
-----------
36   405
-- + --- = 1
81   729
-----------
36   540
-- + --- = 1
81   972
-----------
38   207
-- + --- = 1
61   549
-----------
38   145
-- + --- = 1
76   290
-----------
38   451
-- + --- = 1
76   902
-----------
38   426
-- + --- = 1
95   710
-----------
39   204
-- + --- = 1
51   867
-----------
39   284
-- + --- = 1
65   710
-----------
42   315
-- + --- = 1
87   609
-----------
45   208
-- + --- = 1
61   793
-----------
45   138
-- + --- = 1
90   276
-----------
45   186
-- + --- = 1
90   372
-----------
45   381
-- + --- = 1
90   762
-----------
46   185
-- + --- = 1
92   370
-----------
48   135
-- + --- = 1
96   270
-----------
48   351
-- + --- = 1
96   702
-----------
54   231
-- + --- = 1
87   609
-----------
56   109
-- + --- = 1
84   327
-----------
56   307
-- + --- = 1
84   921
-----------
57   140
-- + --- = 1
92   368
-----------
70   143
-- + --- = 1
96   528
-----------
74   105
-- + --- = 1
89   623
-----------

are all of the fractions of the form you mentioned. Some may be subject to floating-point errors though.