LRT for variance of normal distribution

Derive a likelihood ratio test for H0: σ = σ0 vs. Ha : σ ≠ σ0 for a sample from a normal distribution with unknown mean.

I have found the two likelihood functions that make up the ratio, but I am struggling to simplify it into something understandable.

What have you found so far? Please write down!

-2log⁡(λ)= nlog(σ0)- n/σhat ̂ - nlog(σhat)+ (nσhat)/(σ0^2)

This is the simplest I've gotten it, and it doesn't seem very coherent to me.