rút gọn (căn x)/(căn x -1)-(6 căn x -3)/((căn x -1)(căn x +2))

Với `x >= 0,x \ne 1`. Ta có:

   `(\sqrt{x})/(\sqrt{x}-1)-(6\sqrt{x}-3)/((\sqrt{x} -1)(\sqrt{x} +2))`

`=(\sqrt{x}(\sqrt{x}+2)-6\sqrt{x}+3)/((\sqrt{x}-1)(\sqrt{x}+2))`

`=(x+2\sqrt{x}-6\sqrt{x}+3)/((\sqrt{x} -1)(\sqrt{x} +2))`

`=(x-4\sqrt{x}+3)/((\sqrt{x} -1)(\sqrt{x} +2))`

`=(x-\sqrt{x}-3\sqrt{x}+3)/((\sqrt{x} -1)(\sqrt{x} +2))`

`=((\sqrt{x}-1)(\sqrt{x}-3))/((\sqrt{x} -1)(\sqrt{x} +2))`

`=(\sqrt{x}-3)/(\sqrt{x}+2)`

Giải thích các bước giải:

`(\sqrt{x})/(\sqrt{x}-1)-(6\sqrt{x}-3)/((\sqrt{x}-1)(\sqrt{x}+2))` $(x \geqslant 0; x \ne 1)$

`=(\sqrt{x}(\sqrt{x}+2)-(6\sqrt{x}-3))/((\sqrt{x}-1)(\sqrt{x}+2))`

`=(x+2\sqrt{x}-6\sqrt{x}+3)/((\sqrt{x}-1)(\sqrt{x}+2))`

`=(x-4\sqrt{x}+3)/((\sqrt{x}-1)(\sqrt{x}+2))`

`=(x-\sqrt{x}-3\sqrt{x}+3)/((\sqrt{x}-1)(\sqrt{x}+2))`

`=(\sqrt{x}(\sqrt{x}-1)-3(\sqrt{x}-1))/((\sqrt{x}-1)(\sqrt{x}+2))`

`=((\sqrt{x}-1)(\sqrt{x}-3))/((\sqrt{x}-1)(\sqrt{x}+2))`

`=(\sqrt{x}-3)/(\sqrt{x}+2)`