`\color{#FF0000}{T}\color{#FF7F24}{i}\color{#FFFF00}{t}\color{#7FFF00}{u}\color{#00F5FF}{u}\color{#FF1493}{u}`

$19)$ `P=(x+2)/(x\sqrt{x}-1)+(\sqrt{x}+1)/(x+\sqrt{x}+1)-(\sqrt{x}+1)/(x-1) (0<=x!=1)`

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

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

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

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

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

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

`=(\sqrt{x})/(x+\sqrt{x}+1)`

$20)$ `P=((x\sqrt{x}-1)/(x-\sqrt{x})-(x\sqrt{x}+1)/(x+\sqrt{x})):(1-(3-\sqrt{x})/(\sqrt{x}+1)) (0<x!=1)`

`=[((\sqrt{x}-1)(x+\sqrt{x}+1))/(\sqrt{x}(\sqrt{x}-1))-((\sqrt{x}+1)(x-\sqrt{x}+1))/(\sqrt{x}(\sqrt{x}+1))]:(\sqrt{x}+1-(3-\sqrt{x}))/(\sqrt{x}+1)`

`=((x+\sqrt{x}+1)/(\sqrt{x})-(x-\sqrt{x}+1)/(\sqrt{x})):(\sqrt{x}+1-3+\sqrt{x})/(\sqrt{x}+1)`

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

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

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

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