## Sage – 119

<!-- language: lang-python -->

	x,X=map(int,raw_input().split('/'))
	a=0
	A=c=C=1
	while C<X:
		if c*X>x*C:b,B=c,C
		else:a,A=c,C
		c,C=a+b,A+B
	print a/A,b/B

Sage is only needed in the last line, which takes care of the output. Everything else also works in Python.

This essentially recursively constructs the respective [Farey sequence](http://en.wikipedia.org/wiki/Farey_sequence) using mediants of the existing elements, but restricts itself to those elements closest to the input. From another point of view, it runs a nested-interval search on the respective Farey sequences.