# A lusty summation

Algebra Level 4

$\large \displaystyle \sum_{n=1}^{\infty} \left(\dfrac{4}{n^2+4n+3}-9^{2-n}4^{n+1}\right)$

If the value of above summation can be expressed in the form $$-\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers, find $$m-n$$.

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