Find the value of \[ \frac{5 a}{6\left(a^{2}-1\right)}-\frac{a+3}{2\left(a^{2}+2 a-3\right)}+\fr...

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Find the value of
\[
\frac{5 a}{6\left(a^{2}-1\right)}-\frac{a+3}{2\left(a^{2}+2 a-3\right)}+\frac{a+1}{3 a^{2}+6 a+3}
\]
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