Index: Lib/fractions.py
===================================================================
--- Lib/fractions.py	(revision 71808)
+++ Lib/fractions.py	(working copy)
@@ -103,8 +103,14 @@
 
         if denominator == 0:
             raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
-        numerator = operator.index(numerator)
-        denominator = operator.index(denominator)
+
+        try:
+            numerator, denominator = (
+                numerator.numerator * denominator.denominator,
+                denominator.numerator * numerator.denominator
+                )
+        except AttributeError:
+            raise TypeError("both arguments should be Rational instances")
         g = gcd(numerator, denominator)
         self._numerator = numerator // g
         self._denominator = denominator // g
Index: Lib/test/test_fractions.py
===================================================================
--- Lib/test/test_fractions.py	(revision 71808)
+++ Lib/test/test_fractions.py	(working copy)
@@ -60,12 +60,15 @@
         self.assertEquals((7, 15), _components(F(7, 15)))
         self.assertEquals((10**23, 1), _components(F(10**23)))
 
+        self.assertEquals((3, 77), _components(F(F(3, 7), 11)))
+        self.assertEquals((-9, 5), _components(F(2, F(-10, 9))))
+        self.assertEquals((2486, 2485), _components(F(F(22, 7), F(355, 113))))
+
         self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
                                  F, 12, 0)
         self.assertRaises(TypeError, F, 1.5)
         self.assertRaises(TypeError, F, 1.5 + 3j)
 
-        self.assertRaises(TypeError, F, F(1, 2), 3)
         self.assertRaises(TypeError, F, "3/2", 3)
 
     def testFromString(self):