gh-35220: add tests for solved issue about fraction fields
    
### 📚 Description

Add a simple test for #15971.

Closes #15971.

### 📝 Checklist

- [x] I have made sure that the title is self-explanatory and the
description concisely explains the PR.
- [x] I have linked an issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation accordingly.
    
URL: #35220
Reported by: Vincent Delecroix
Reviewer(s): Frédéric Chapoton

Author: Release Manager

src/sage/rings/fraction_field.py

@@ -55,6 +55,18 @@
     sage: F = FractionField(PolynomialRing(RationalField(),2,'x'))
     sage: F == loads(dumps(F))
     True
+
+Test that :trac:`15971` is fixed::
+
+    sage: for B in [QQ['t'], QQ['s, t'], ZZ['t'], ZZ['s, t']]:
+    ....:     F = B.fraction_field()
+    ....:     R = F['x, y']
+    ....:     x = R.gen(0)
+    ....:     print(x / x)
+    1
+    1
+    1
+    1
 """
 # ****************************************************************************
 #