81 chars:
$ perl -e '($n,$d)=split"/",pop;{1while++$x<$d/$n;warn"1/$x\n";$n=$n*$
+x-$d;$d*=$x;redo if$n}' 18/20
1/2
1/3
1/15
Update: changing the entire structure to a C-style for-loop saves 2 chars, so this gives me a 79-char solution:
for(($n,$d)=split"/",pop;$n;){1while++$x<$d/$n;warn"1/$x\n";$n=$n*$x-$
+d;$d*=$x}
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