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

Với : `x>0,xne1,xne4`

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

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

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

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

`b)` 

Để `A=-2/3` 

`<=>(\sqrt{x}-2)/\sqrt{x}=-2/3`  Với : `x>0,xne1,xne4`

`<=>3.(\sqrt{x}-2)=-2\sqrt{x}`

`<=>3\sqrt{x}-6=-2\sqrt{x}`

`<=>3\sqrt{x}+2\sqrt{x}=6`

`<=>5\sqrt{x}=6`

`<=>\sqrt{x}=6/5`

`<=>(\sqrt{x})^2=(6/5)^2`

`<=>x=36/25` ( thỏa mãn)

Vậy để `A=-2/3` thì `x=36/25`

Đáp án:

 #Wan 

`A = (1/(x-2sqrt(x)) - 1/(sqrt(x)-2)) : (1-sqrt(x))/(x-4sqrt(x)+4) (DK : x > 0 ; x \ne 1 ; x \ne 4)`

`A = (1/[sqrt(x)(sqrt(x)-2)] - (sqrt(x))/[sqrt(x)(sqrt(x)-2) )): (1-sqrt(x))/(x-4sqrt(x)+4)`

`A = (1-sqrt(x))/[sqrt(x)(sqrt(x)-2)].[(sqrt(x)-2)^2]/(1-sqrt(x))`

`A = (sqrt(x)-2)/(sqrt(x))`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`A = -2/3 (x > 0 ; x \ne 1 ; x \ne 4)`

`=> (sqrt(x)-2)/(sqrt(x)) = -2/3`

`<=> 3(sqrt(x)-2) = -2sqrt(x)`

`<=> 3sqrt(x) - 6 + 2sqrt(x) = 0`

`<=> 5sqrt(x) = 6`

`<=> sqrt(x) = 6/5`

`<=> x = 36/25 (t//m)`

`=> x = 36/25` thi `A = -2/3`

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