How to simplify or reduce $$\left(\frac{\left(\mathbf{1}^\top\mathbf{\Sigma}^{-1}\boldsymbol\mu \right)^2}{\mathbf{1}^\top\mathbf{\Sigma}^{-1}\boldsymbol{1} \cdot \boldsymbol\mu ^\top\mathbf{\Sigma}^{-1}\boldsymbol\mu }\right)$$
whose terms can be grouped as $\frac{b^2}{a\cdot c}$ if it helps any. Here are the dimensions of the vectors and matrices for some integer $N$:
- $\mathbf{1}\in \mathbb{R}^{N\times 1}$ is a vector of ones
- $\boldsymbol\mu \in \mathbb{R}^{N\times 1}$ is a vector of real values
- $\mathbf{\Sigma}\in \mathbb{R}^{N\times N}$ is the covariance matrix
I'm also interested in the steps towards reduction.