$P=.....=\frac{x-1}{\sqrt{x}} : (\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}.(\sqrt{x}+1)}+\frac{1-\sqrt{x}}{\sqrt{x}.(\sqrt{x}+1)}) = \frac{x-1}{\sqrt{x}}:\frac{x-1+1-\sqrt{x}}{\sqrt{x}.(\sqrt{x}+1)} = \frac{x-1}{\sqrt{x}}:\frac{x-\sqrt{x}}{\sqrt{x}.(\sqrt{x}+1)} = \frac{x-1}{\sqrt{x}}.\frac{\sqrt{x}+1}{\sqrt{x}-1} = \frac{(x-1)(\sqrt{x}+1)}{\sqrt{x}(\sqrt{x}-1)}$