P=$(\frac{(x+2)}{(\sqrt{x}+1)-\sqrt{2})}{((\sqrt{x}-4)/(1-x)}-(\sqrt{x})/(\sqrt{x}+1))

=(x+2-\sqrt{x}.(\sqrt{x}+1))/(\sqrt{x}+1):(\sqrt{x}-4-\sqrt{x}.(1-\sqrt{2}))/(1-x)

=(x+2-x-\sqrt{x})/(\sqrt{x}+1).((\sqrt{x}+1).(1-\sqrt{x}))/(\sqrt{x}-4-\sqrt{x}+x)

=((2-\sqrt{x}).(1-\sqrt{x}))/(-(2-\sqrt{x}).(2+\sqrt{x})

=(\sqrt{x}-1)/(2+\sqrt{x})$