Being $ p, q, r, s, t \in \mathbb {R} ^ * _ {+} $ and knowing that
$\begin{cases} p^2+pq+q^2=s^2\\ q^2+qr+r^2=t^2 \\ r^2+rp+p^2=s^2-st+t^2\\ \end{cases}$
Prove that
$\frac{s^2-st+t^2}{s^2t^2}=\frac{r^2}{q^2t^2}+\frac{p^2}{q^2s^2}-\frac{pr}{q^2ts}$
What I tried: I was trying the obvious, he already gives the numerator, $s ^ 2 $ and $ t ^ 2,$ so theoretically the only job was to make the product.
I noticed that it gives some things like: $ (a + b) ^ 2-ab $, or $(a-b) ^ 2 + ab$ too, but it didn't help much.
$$s^2+t^2-(s^2-st+t^2)=?$$
We already have $$s^2+t^2=?$$
Just replace the values of $$s^2+t^2,st$$