Đáp án+Giải thích các bước giải:
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`1/(sqrtx-sqrt{x-1})-(x-3)/(sqrt{x-1}-2)`
`=(x-(x-1))/(sqrtx-sqrt{x-1})-(x-1-2)/(sqrt{x-1}-2)`
`=((sqrtx-sqrt{x-1})(sqrtx+sqrt{x-1}))/(sqrtx-sqrt{x-1})-((sqrt{x-1}-sqrt2)(sqrt{x-1}+sqrt2))/(sqrt{x-1}-sqrt2)`
`=sqrt{x}+sqrt{x-1}-(sqrt{x-1}+sqrt2)`
`=sqrt{x}+sqrt{x-1}-sqrt{x-1}-sqrt2`
`=sqrtx-sqrt2`
`2/(sqrt2-sqrtx)-(sqrtx+sqrt2)/(sqrt{2x}-x)`
`=2/(sqrt2-sqrtx)-(sqrtx+sqrt2)/(sqrtx(sqrt2-sqrtx))`
`=(2sqrtx-sqrtx-sqrt2)/(sqrtx(sqrt2-sqrtx))`
`=(sqrtx-sqrt2)/(-sqrtx(sqrtx-sqrt2))`
`=-1/sqrtx`
`=>A=(1/(sqrtx-sqrt{x-1})-(x-3)/(sqrt{x-1}-2))(2/(sqrt2-sqrtx)-(sqrtx+sqrt2)/(sqrt{2x}-x))`
`=(sqrtx-sqrt2)*-1/sqrtx`
`=(-(sqrtx-sqrt2))/sqrtx`
`b)x=3-2sqrt2=(sqrt2-1)^2`
`=>A=(-(sqrt2-1-sqrt2))/(sqrt2-1)`
`A=1/(sqrt2-1)=sqrt2+1`