$\begin{array}{l}P = \left(\dfrac{3}{x-1} + \dfrac{1}{\sqrt x + 1}\right):\dfrac{1}{\sqrt x + 1}\qquad (x \geq 0;\, x \ne 1)\\ \to P = \dfrac{3}{x-1}:\dfrac{1}{\sqrt x + 1} + 1\\ \to P = \dfrac{3}{(\sqrt x + 1)(\sqrt x - 1)} \cdot (\sqrt x + 1) + 1\\ \to P = \dfrac{3}{\sqrt x - 1} + 1\\ \to P = \dfrac{3 + \sqrt x - 1}{\sqrt x - 1}\\ \to P = \dfrac{\sqrt x + 2}{\sqrt x - 1}\end{array}$
