Đáp án:

`B=((x\sqrt{x}-1)/(x-\sqrt{x})-(x\sqrt{x}+1)/(x+\sqrt{x})):(2x-4\sqrt{x}+2)/(x-1)` `(x>0;x\ne1)`

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

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

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

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

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

Đáp án:

Vậy `B=(\sqrtx+1)/(\sqrt{x}-1)` với `x>0;x ne 1` 

Giải thích các bước giải:

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

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

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

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

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

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

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

Vậy `B=(\sqrtx+1)/(\sqrt{x}-1)` với `x>0;x ne 1`