Simplification of integral with division between summations

Question

Considering that

$$\sum_{j = 0}^{\infty} \int f_j(x) < \infty$$ and $$\sum_{j = 0}^{\infty} \int g_j(x) < \infty$$, $\forall x \in \mathrm{R} : f(x) \gt 0, g(x) \gt 0$. How can I simplify the following expression ?

$$ \int \frac{\sum_{j = n}^N f_j(x)}{\sum_{j = n}^N g_j(x)} dx $$

Answer 1

how can I simplify the following expression ? $$\int \frac{\sum_{j = n}^N f_j(x)}{\sum_{j = n}^N g_j(x)} dx$$

You cannot, without some assumptions that relate $f_j$ to $g_j$. (Or, what Did said in a comment.)