diff --git a/Lib/test/test_unittest.py b/Lib/test/test_unittest.py
index 5c3921d..2fab7de 100644
--- a/Lib/test/test_unittest.py
+++ b/Lib/test/test_unittest.py
@@ -2989,6 +2989,11 @@
         self.assertRaises(self.failureException,
                           self.assertNotAlmostEqual, 0, .1+.1j, places=0)
 
+        self.assertAlmostEqual(float('inf'), float('inf'))
+        self.assertRaises(self.failureException, self.assertNotAlmostEqual,
+                          float('inf'), float('inf'))
+
+
     def test_assertRaises(self):
         def _raise(e):
             raise e
diff --git a/Lib/unittest/case.py b/Lib/unittest/case.py
index d52bc8d..cac2842 100644
--- a/Lib/unittest/case.py
+++ b/Lib/unittest/case.py
@@ -457,7 +457,13 @@
 
            Note that decimal places (from zero) are usually not the same
            as significant digits (measured from the most signficant digit).
+
+           If the two objects compare equal then they will automatically
+           compare almost equal.
         """
+        if first == second:
+            # shortcut for ite
+            return
         if round(abs(second-first), places) != 0:
             standardMsg = '%r != %r within %r places' % (first, second, places)
             msg = self._formatMessage(msg, standardMsg)
@@ -470,8 +476,10 @@
 
            Note that decimal places (from zero) are usually not the same
            as significant digits (measured from the most signficant digit).
+
+           Objects that are equal automatically fail.
         """
-        if round(abs(second-first), places) == 0:
+        if (first == second) or round(abs(second-first), places) == 0:
             standardMsg = '%r == %r within %r places' % (first, second, places)
             msg = self._formatMessage(msg, standardMsg)
             raise self.failureException(msg)