c) \(\left(\dfrac{\sqrt{x}}{2\sqrt{x}-2}-\dfrac{\sqrt{x}}{2\sqrt{x}+2}\right):\dfrac{\sqrt{x}}{x+2\sqrt{x}+1}\)
= \(\left(\dfrac{\sqrt{x}}{2\left(\sqrt{x}-1\right)}-\dfrac{\sqrt{x}}{2\left(\sqrt{x}+1\right)}\right):\dfrac{\sqrt{x}}{\sqrt{x}^2+2\sqrt{x}+1^2}\)
= \(\left(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\) \(:\dfrac{\sqrt{x}}{\left(\sqrt{x}+1\right)^2}\)
= \(\left(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)-\sqrt{x}\left(\sqrt{x}-1\right)}{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\) \(.\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}}\)
= \(\dfrac{2\sqrt{x}}{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}}\)
= \(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
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