The method to divide fractions is to keep the first fraction the same, turn the divide sign into a multiply and turn the second fraction upside down. This is known as multiplying by the reciprocal.

Let 𝐾 be a number field with algebraic closure K¯, and let 𝑆 be a finite set of places of 𝐾 containing all the infinite ones. Let Γ₀ be a finitely generated subgroup of Gm(K¯), and let Γ⊂Gm(K¯) be ...