Egyptian Fractions

Python 2, 169 167 chars

x,y=input()
def R(n,a,b):
 if n<2:return[b/a][b%a:]
 for m in range((b+a-1)/a,b*n/a):
  L=R(n-1,a*m-b,m*b)
  if L:return[m]+L
n=L=0
while not L:n+=1;L=R(n,x,y)
print L

Takes comma-separated args on stdin and prints a python list on stdout.

$ echo 8,11 | ./egypt.py 
[2, 5, 37, 4070]

Common Lisp, 137 chars

(defun z(n)(labels((i(n s r)(cond((= n 0)r)((< n(/ 1 s))(i n(ceiling(/ 1 n))r))(t(i(- n(/ 1 s))(1+ s)(cons s r))))))(reverse(i n 2'()))))

(z 43/48) -> (2 3 16)

(z 8/11) -> (2 5 37 4070)

(z 5/121) -> (25 757 763309 873960180913 1527612795642093418846225)

No need to worry about huge numbers, or handling fractional notation!

PHP 82 bytes

<?for(fscanf(STDIN,"%d%d",$a,$b);$a;)++$i<$b/$a||printf("$i ",$a=$a*$i-$b,$b*=$i);

This could be made shorter, but the current numerator and denominator need to be keep as whole numbers to avoid floating point rounding error (instead of keeping the current fraction).

Sample usage:

$ echo 43 48 | php egyptian-fraction.php
2 3 16
$ echo 8 11 | php egyptian-fraction.php
2 5 37 4070