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$\begin{array}{l} \left(\dfrac{x - \sqrt{x}}{\sqrt{x} - 1} - 2\right) \cdot \left(\dfrac{x + \sqrt{x}}{\sqrt{x} + 1} + 2\right) \\ = \left[\dfrac{\sqrt{x}(\sqrt{x} - 1)}{\sqrt{x} - 1} - 2\right] \cdot \left[\dfrac{\sqrt{x}(\sqrt{x} + 1)}{\sqrt{x} + 1} + 2\right] \\ = (\sqrt{x} - 2)(\sqrt{x} + 2) \\ = (\sqrt{x})^2 - 2^2 \\ = x - 4 \end{array}$