If $\alpha, \beta, \gamma $ and $\delta$ be the roots of the equation $x^4+px^3+qx^2+rx+s=0$, $s\neq 0$, find the value of symmetric function $$\sum{\frac{\alpha\beta}{\gamma^2}}$$
We have $\sum \alpha =-p, ~~~~\sum\alpha\beta=q, ~~~\sum \alpha\beta\gamma =-r$ and $\alpha\beta\gamma\delta=s$. But how to use them to get the desired result. Please help.
I wrote $$\sum{\frac{\alpha\beta}{\gamma^2}}=\frac{\sum\alpha^3\beta^3\delta^2}{s^2}$$ But I think it becoms more complicated.