\(\left(1+\dfrac{x+\sqrt{x}}{1+\sqrt{x}}\right).\left(1+\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\right)\\ =\left(1+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{1+\sqrt{x}}\right).\left(1+\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{1-\sqrt{x}}\right)\\ =\left(1+\sqrt{x}\right).\left(1-\sqrt{x}\right)\\ =1-x\)