diff --git a/src/polyform.jl b/src/polyform.jl
index 09c871fa5..873e332a8 100644
--- a/src/polyform.jl
+++ b/src/polyform.jl
@@ -81,14 +81,15 @@ end
 # forward gcd
 
 PF = :(PolyForm{promote_symtype(/, symtype(x), symtype(y))})
+const FriendlyCoeffType = Union{Integer, Rational}
 @eval begin
     Base.div(x::PolyForm, y::PolyForm) = $PF(div(x.p, y.p), mix_dicts(x, y)...)
-    Base.div(x::Integer, y::PolyForm)  = $PF(div(x, y.p), y.pvar2sym, y.sym2term)
-    Base.div(x::PolyForm, y::Integer)  = $PF(div(x.p, y), x.pvar2sym, x.sym2term)
+    Base.div(x::FriendlyCoeffType, y::PolyForm)  = $PF(div(x, y.p), y.pvar2sym, y.sym2term)
+    Base.div(x::PolyForm, y::FriendlyCoeffType)  = $PF(div(x.p, y), x.pvar2sym, x.sym2term)
 
     Base.gcd(x::PolyForm, y::PolyForm) = $PF(_gcd(x.p, y.p), mix_dicts(x, y)...)
-    Base.gcd(x::Integer, y::PolyForm)  = $PF(_gcd(x, y.p), y.pvar2sym, y.sym2term)
-    Base.gcd(x::PolyForm, y::Integer)  = $PF(_gcd(x.p, y), x.pvar2sym, x.sym2term)
+    Base.gcd(x::FriendlyCoeffType, y::PolyForm)  = $PF(_gcd(x, y.p), y.pvar2sym, y.sym2term)
+    Base.gcd(x::PolyForm, y::FriendlyCoeffType)  = $PF(_gcd(x.p, y), x.pvar2sym, x.sym2term)
 end
 
 _isone(p::PolyForm) = isone(p.p)
diff --git a/test/polyform.jl b/test/polyform.jl
index 4500763e9..9fb088a7f 100644
--- a/test/polyform.jl
+++ b/test/polyform.jl
@@ -63,6 +63,9 @@ end
     ##404#issuecomment-939404030
     a = 1 / (x - (2//1)) + ((-5//1) - x) / ((x - (2//1))^2)
     @test isequal(simplify_fractions(a), -7/(x-2)^2)
+
+    # https://github.com/JuliaSymbolics/Symbolics.jl/issues/968
+    @eqtest simplify_fractions((x * y + (1//2) * x) / (2 * x)) == 1//4 * (1 + 2y)
 end
 
 @testset "isone iszero" begin