diff --git a/fastapi/middleware/asyncexitstack.py b/fastapi/middleware/asyncexitstack.py
index 7d34aa9ed..808da413c 100644
--- a/fastapi/middleware/asyncexitstack.py
+++ b/fastapi/middleware/asyncexitstack.py
@@ -1,5 +1,4 @@
 from contextlib import AsyncExitStack
-from typing import Optional
 
 from starlette.types import ASGIApp, Receive, Scope, Send
 
@@ -10,16 +9,6 @@ class AsyncExitStackMiddleware:
         self.context_name = context_name
 
     async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
-        dependency_exception: Optional[Exception] = None
         async with AsyncExitStack() as stack:
             scope[self.context_name] = stack
-            try:
-                await self.app(scope, receive, send)
-            except Exception as e:
-                dependency_exception = e
-                raise e
-        if dependency_exception:
-            # This exception was possibly handled by the dependency but it should
-            # still bubble up so that the ServerErrorMiddleware can return a 500
-            # or the ExceptionMiddleware can catch and handle any other exceptions
-            raise dependency_exception
+            await self.app(scope, receive, send)