Answer
$-6s^2t-6r^2t+4st^2$
Work Step by Step
By combining like terms, the given expression, $
3s^2t+r^2t-9ts^2-st^2+5t^2s-7tr^2
,$ simplifies to
\begin{array}{l}\require{cancel}
3s^2t+r^2t-9s^2t-st^2+5st^2-7r^2t
\\\\=
(3s^2t-9s^2t)+(r^2t-7r^2t)+(-st^2+5st^2)
\\\\=
-6s^2t-6r^2t+4st^2
.\end{array}