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use Junk;do

#!/usr/bin/perl -l
pop=~m|/|;($f,$g)=($`,$');sub d{int($_[1]/$_[0]+1)}sub
...
for($p,$l){$_/=$g};($p,$l)}while($f>1){push@o,"1/".d(#
$f,$g);($f,$g)=re($f,$g,1,d($f,$g));}print join' + ',#
@o,"$f/$g";# ungolfed and thus not for production use!

($z,$n)=($_=pop)=~/(.+)\/(.+)/;$s='==';for(;;){$m=int($n/$z+1);$_
.=" $s 1/".($z==1?$n:$m);$z<=1&&last;($z,$n)=($z*$m-$n,$m*$n);($x
,$y)=($z,$n);($x,$y)=($y,$x%$y)while$y;$z/=$x;$n/=$x;$s='+'}print

qwurx [shmem] ~> perl -l egy.pl 2355/12344
2355/12344 == 1/6 + 1/42 + 1/3282 + 1/15755059 + 1/744665636525384