In the overlapping triangles $△PQR$ and $△PQS$ sharing common side $PQ$, $\angle SPQ$ and $\angle RQP$ are right angles. If $PQ=6$, $QR=3$, $PS=9$, and $\overline{PR}$ and $\overline{QS}$ intersect at $T$, what is the difference between the areas of $△PST$ and $△RQT$?
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