`a)ĐKXĐ: x>0; x\ne1`
`P=1/(\sqrt{x}+1)+x/(\sqrt{x}-x)`
`P=1/(\sqrt{x}+1)+(\sqrt{x})^2/(\sqrt{x}(1-\sqrt{x}))`
`P=1/(\sqrt{x}+1)+\sqrt{x}/(1-\sqrt{x})`
`P=((1-\sqrt{x})+\sqrt{x}(\sqrt{x}+1))/((\sqrt{x}+1)(1-\sqrt{x}))`
`P=(1-\sqrt{x}+x+\sqrt{x})/(1-x)`
`P=(1+x)/(1-x)`
Vậy với `x>0; x\ne1` thì `P=(1+x)/(1-x)`
`b)`Thay `x=1/\sqrt{2}(TM)` vào `P` ta được:
$P=\dfrac{1+\dfrac{1}{\sqrt{2}}}{1-\dfrac{1}{\sqrt{2}}}$
$P=\dfrac{\dfrac{2+\sqrt{2}}{2}}{\dfrac{2-\sqrt{2}}{2}}$
`P=(2+\sqrt{2})/(2-\sqrt{2})`
`P=((2+\sqrt{2})(2+\sqrt{2}))/((2-\sqrt{2})(2+\sqrt{2}))`
`P=(2+\sqrt{2})^2/(4-2)`
`P=(4+4\sqrt{2}+2)/2`
`P=(6+4\sqrt{2})/2`
`P=(2(3+2\sqrt{2}))/2`
`P=3+2\sqrt{2}`
Vậy với `x=1/\sqrt{2}` thì `P=3+2\sqrt{2}`
