Đáp án:+Giải thích các bước giải:

3, a, `P=(\sqrtx-1/\sqrtx):((\sqrtx-1)/\sqrtx + (1-\sqrtx)/(x+\sqrtx))`

`= (x-1)/\sqrtx:((\sqrtx-1)/\sqrtx+(1-\sqrtx)/(\sqrtx(\sqrtx+1)))`

`=(x-1)/\sqrtx: ((\sqrtx-1)(\sqrtx+1)+1-\sqrtx)/(\sqrtx(\sqrtx+1))`

`=(x-1)/\sqrtx : (x-1+1-\sqrtx)/(\sqrtx(\sqrtx+1))`

`=(x-1)/\sqrtx:(x-\sqrtx)/(\sqrtx(\sqrtx+1))`

`=(x-1)/\sqrtx : (\sqrtx(\sqrtx-1))/(\sqrtx(\sqrtx+1))`

`=(x-1)/\sqrtx : (\sqrtx-1)/(\sqrtx+1)`

`=((\sqrtx+1)(\sqrtx-1))/\sqrtx . (\sqrtx+1)/(\sqrtx-1)`

`=(\sqrtx+1)^2/\sqrtx`

b, Ta có: `x=2/(2+\sqrt3)=(2(2-\sqrt3))/((2+\sqrt3)(2-\sqrt3))=(4-2\sqrt3)/(2^2-(\sqrt3)^2)`

`=((\sqrt3)^2-2.\sqrt3.1+1)/1=(\sqrt3-1)^2`

`=> \sqrtx = \sqrt((\sqrt3-1)^2=\sqrt3-1`

`=>P=(\sqrtx+1)^2/\sqrtx=(\sqrt3-1+1)^2/(\sqrt3-1)=(\sqrt3)^2/(\sqrt3-1)`

`=((\sqrt3)^2.(\sqrt3+1))/((\sqrt3-1)(\sqrt3+1))`

`=(3(\sqrt3+1))/((\sqrt3)^2-1^2)=(3\sqrt3+3)/2`

4, a, `A=( (\sqrtx+\sqrty)^2-4\sqrt(xy))/(\sqrtx-\sqrty).\sqrt(xy)/(x\sqrty+y\sqrtx)`

`= (x+2\sqrt(xy)+y-4\sqrt(xy))/(\sqrtx-\sqrty). \sqrt(xy)/(\sqrt(xy)(\sqrtx+\sqrty)`

`=(x-2\sqrt(xy)+y)/(\sqrtx-\sqrty). 1/(\sqrtx+\sqrty)`

`=(\sqrtx-\sqrty)^2/((\sqrtx-\sqrty)(\sqrtx+\sqrty)`

`=(\sqrtx-\sqrty)/(\sqrtx+\sqrty)`

b, `A = (\sqrtx-\sqrty)/(\sqrtx+\sqrty) = (\sqrtx-\sqrty)^2/(x-y)`

`x=\sqrt(2+\sqrt3)=> \sqrt2x=\sqrt(4+2\sqrt3)=\sqrt((\sqrt3+1)^2)=\sqrt3+1`

`=> x = (\sqrt3+1)/\sqrt2`

`y=\sqrt(2-\sqrt3) => \sqrt2y=\sqrt(4-2\sqrt3)=\sqrt((\sqrt3-1)^2)=\sqrt3-1`

`=> y = (\sqrt3-1)/\sqrt2`

`=> x-y= (\sqrt3+1)/\sqrt2 - (\sqrt3-1)/\sqrt2=2/\sqrt2=\sqrt2`

`(\sqrtx-\sqrty)^2=x-2\sqrt(xy)+y=(\sqrt3+1)/\sqrt2+(\sqrt3-1)/\sqrt2-2\sqrt{((\sqrt3+1)(\sqrt3-1))/2}`

`=(2\sqrt3)/2-2=\sqrt6-2`

`=> A = (\sqrt6-2)/\sqrt2=(\sqrt2(\sqrt3-\sqrt2))/\sqrt2=\sqrt3-\sqrt2 `