# Almost a geometric series, but not quite

Algebra Level 4

Let $$f : (-1, 1) \to \mathbb{R}$$ be defined as $$\displaystyle f(x) = \sum_{n=1}^{\infty} nx^n$$.

Find the value of $$\dfrac{1}{f \left(\dfrac{1}{5} \right) + f \left(-\dfrac{1}{3} \right)}$$.

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