I want to compute the following limit

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> $$\lim\_{x\to 3}\frac{1}{(9-x^2)^2}\left( \frac{9+x^2}{3x}-2\sin \frac{3π}{2}\sin\frac{πx}{2}\right)$$
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But I am looking for a more elegant way not using L'Hopital rule. especially squeezing will be good and welcome.