`1)P=sqrty/(sqrt(xy)-x)-sqrtx/(y-sqrt(xy)) (x>0;y>0;xney)`

`=sqrty/(sqrt(x)(sqrty-sqrtx))-sqrtx/(sqrty(sqrty-sqrtx))`

`=(y-x)/(sqrt(xy).(sqrty-sqrtx))`

`=(sqrtx+sqrty)/sqrt(xy)`

`2)P=(sqrtx/sqrty-3):sqrt(xy)/(x+3sqrt(xy))(x>0;y>0)`

`=(sqrtx-3sqrty)/sqrty . (sqrtx(sqrtx+3sqrty))/sqrt(xy)`

`=(x-9y)/y`

`3)P=((xsqrtx-ysqrty)/(sqrtx-sqrty)+sqrt(xy)) :(x-y)`

`=(x+sqrt(xy)+y+sqrt(xy))/((sqrtx-sqrty)(sqrtx+sqrty))`

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

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

`4)P=(1+sqrtx/(sqrtx+x+1)) : (sqrtx+1)/(xsqrtx-1)`

`=(x+2sqrtx+1)/(x+sqrtx+1) . ((sqrtx-1)(x+sqrtx+1))/(sqrtx+1)`

`=x-1`

`5)((sqrtx-1)/(sqrtx+1)+(2sqrtx)/(sqrtx-1)-(3sqrtx-1)/(1-x)).(2/sqrtx-2/x)`

`=(x-2sqrtx+1+2x+2sqrtx+3sqrtx-1)/((sqrtx-1)(sqrtx+1)) . (2(sqrtx-1))/x`

`=(3x+3sqrtx)/(sqrtx+1). 2/x`

`=6`