diff --git a/test/rational.jl b/test/rational.jl
index 52f502b4178a6..52deb31047d67 100644
--- a/test/rational.jl
+++ b/test/rational.jl
@@ -34,6 +34,7 @@ using Test
     @test_throws InexactError rationalize(Int, NaN)
     # issue 32569
     @test_throws ArgumentError 1 // typemin(Int)
+    @test_throws ArgumentError 0 // 0
     @test -2 // typemin(Int) == -1 // (typemin(Int) >> 1)
     @test 2 // typemin(Int) == 1 // (typemin(Int) >> 1)
 
@@ -394,6 +395,7 @@ end
     @test gcdx(1//2, 1//0) == (1//0, 0, 1)
     @test gcdx(1//0, 1//0) == (1//0, 1, 1)
     @test gcdx(1//0, 0//1) == (1//0, 1, 0)
+    @test gcdx(0//1, 0//1) == (0//1, 1, 0)
 
     @test gcdx(1//3, 2) == (1//3, 1, 0)
     @test lcm(1//3, 1) == 1//1