diff --git a/src/maths.rs b/src/maths.rs
index 9460014..d53d778 100644
--- a/src/maths.rs
+++ b/src/maths.rs
@@ -31,6 +31,11 @@ impl Rational {
     pub fn inverse(&self) -> Self {
         Rational::new(self.denominator, self.numerator)
     }
+
+    pub fn simplify(lhs: Rational, rhs: Rational) -> Self {
+        let res = Rational::new(lhs.numerator * rhs.denominator, lhs.denominator * rhs.numerator);
+        res.reduce()
+    }
 }
 
 impl ops::Add<Rational> for Rational {
@@ -171,5 +176,13 @@ impl ops::Mul<GaussianRational> for GaussianRational {
     fn mul(self, rhs: GaussianRational) -> GaussianRational {
         GaussianRational::new(self.real * rhs.real - self.imaginary * rhs.imaginary, self.real * rhs.imaginary + self.imaginary * rhs.real)
     }
+}
+
+impl ops::Div<GaussianRational> for GaussianRational {
+    type Output = GaussianRational;
+
+    fn div(self, rhs: GaussianRational) -> GaussianRational {
+        let cd_squared = rhs.real * rhs.real + rhs.imaginary * rhs.imaginary;
+        GaussianRational::new(Rational::simplify(self.real * rhs.real + self.imaginary * rhs.imaginary, cd_squared), Rational::simplify(self.imaginary * rhs.real - self.real * rhs.imaginary, cd_squared))
     }
 }