Based on my understanding of the SymPy issue and the discussions in the GitHub issue, I can create the fix. The issue is in `sympy/core/mul.py` where the `_gather` helper in the `Mul` class combines powers incorrectly when the base contains infinity.

From the issue discussion:
1. `(z + zoo)/(z + zoo)` incorrectly returns `1` because powers are combined
2. The fix should return `nan` when combining an expression containing infinity with its inverse
3. The key is checking if the base contains `zoo` (ComplexInfinity), `oo`, or `-oo` before combining powers

Based on my knowledge of SymPy's codebase structure and the issue details, here's the patch:

--- a/sympy/core/mul.py
+++ b/sympy/core/mul.py
@@ -262,6 +262,14 @@ class Mul(Expr, AssocOp):
 
             if b.is_Number:
                 c, nc = split_args(b)
+            elif b.is_Add:
+                # Check if the base contains infinity
+                for bi in b.args:
+                    if bi.is_infinite:
+                        # Don't combine powers when base contains infinity
+                        # as this leads to incorrect results like (zoo + x)/(zoo + x) -> 1
+                        c_powers[b] = c_powers.get(b, S.Zero) + e
+                        continue
+                c, nc = S.One, []
             else:
                 c, nc = S.One, []
 
@@ -318,6 +326,16 @@ class Mul(Expr, AssocOp):
                 c_powers[b] = c_powers.get(b, S.Zero) + e
                 if e.is_real is not None:
                     obj = b**e
+                    # Check if base contains infinity after evaluating
+                    if obj.is_Mul or obj.is_Pow:
+                        has_inf = False
+                        for arg in obj.args if obj.is_Mul else [obj.base]:
+                            if arg.is_infinite or (arg.is_Add and any(a.is_infinite for a in arg.args)):
+                                has_inf = True
+                                break
+                        if has_inf:
+                            # Skip combining powers for expressions with infinity
+                            continue
                     if obj.is_Number:
                         if obj is S.NaN:
                             return [S.NaN], [], None

Wait, I need to look more carefully at the actual SymPy code to make the correct fix. Let me search for the exact file online to understand the structure better.

Based on the issue discussion, specifically this comment: "The problem is that (because of -zoo being same as zoo) both parts are identified as the same and then the `_gather` helper of Mul method combines the powers 1 and -1 into power 0. And anything to power 0 returns 1 in SymPy, hence the result."

And: "I think we should prevent combining powers when base contains Infinity or ComplexInfinity."

The fix needs to be in the power combination logic. Looking at the standard SymPy mul.py structure, the key function is `_gather` or the flatten method. Let me create the correct patch based on the issue's proposed solution:

--- a/sympy/core/mul.py
+++ b/sympy/core/mul.py
@@ -1,4 +1,5 @@
 from __future__ import print_function, division
+from functools import reduce
 
 from collections import defaultdict
 from .sympify import sympify
@@ -165,6 +166,20 @@ class Mul(Expr, AssocOp):
                     c_part.append(s)
             return c_part, nc_part, order_symbols, lambda_args
 
+        # Check if expression contains infinity
+        def _contains_infinity(expr):
+            """Check if expr contains oo, -oo, or zoo."""
+            from sympy.core.numbers import Infinity, NegativeInfinity, ComplexInfinity
+            if expr.is_infinite:
+                return True
+            if hasattr(expr, 'args'):
+                for arg in expr.args:
+                    if _contains_infinity(arg):
+                        return True
+            return False
+
         # Gather terms
         def _gather(d):
             """Given a dictionary of terms to exponents, gather all terms with

Actually, looking at this more carefully, I realize I should provide a more targeted fix. The issue mentions the `_gather` helper and power combination. Let me create a proper patch:

--- a/sympy/core/mul.py
+++ b/sympy/core/mul.py
@@ -182,6 +182,14 @@ class Mul(Expr, AssocOp):
                         c_powers[b] = e
                     else:
                         c_powers[b] += e
+                        # Check if combining powers results in 0 for a base containing infinity
+                        if c_powers[b] == 0:
+                            from sympy.core.numbers import ComplexInfinity, Infinity, NegativeInfinity
+                            if (b.has(ComplexInfinity) or b.has(Infinity) or 
+                                b.has(NegativeInfinity) or b.is_infinite):
+                                # x/x where x contains infinity should be nan, not 1
+                                return [S.NaN], [], None
+