On the Diophantine equation \({y^{p} = \frac{f(x)}{g(x)}}\)

We consider the Diophantine equation $$y^{p} = \frac{f(x)}{g(x)},$$ where \({x \in \mathbb{Z}}\) and \({y \in \mathbb{Q}}\) are unknowns, f(x) and g(x) are non-zero integer polynomials in variable x and p is prime. We give bounds for x, when \({(x, y) \in \mathbb{Z} \times \mathbb{Q}}\) is a solution of the equation. This improves the results of some recent papers.