Calculate sum of series ‎$‎\sum_{n=1}^\infty ‎\frac{x+a}{n(x+a) + n^2}‎$. ‎I've been stuck with calculating the sum of series of the following problem. Can you help me?‎

$$\sum_{n=1}^\infty ‎\frac{x+a}{n(x+a) + n^2}‎$$

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for real ‎numbers ‎‎$‎a\geq 0‎$ ‎and ‎‎$‎x\geq 1‎$‎.
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After @URL's comment, using
$$S_p=\sum_{n=1}^p\frac{x+a}{n(x+a)+n^2}=\sum_{n=1}^p\frac1n-\sum_{n=1}^p\frac1{n+(x+a)}$$ and using generalized harmonic numbers, we have
$$S_p=H_{a+x}+H_p-H_{a+x+p}$$
Now, using the asymptotics
$$H_q=\gamma +\log \left({q}\right)+\frac{1}{2 q}-\frac{1}{12
   q^2}+O\left(\frac{1}{q^3}\right)$$ and using it for the second an third term, we end with
$$S_p=H_{a+x}-\frac{a+x}{p}+O\left(\frac{1}{p^2}\right)$$
