Question

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Answer 1

`3/((x-1)(x-2))-2/((x-1)(x-3))=1/((x-2)(x-3))` (ĐK: `x<>1;x<>2;x<>3`)

`<=>(3(x-3))/((x-1)(x-2)(x-3))-(2(x-2))/((x-1)(x-2)(x-3))=(x-1)/((x-1)(x-2)(x-3))`

`<=>3(x-3)-2(x-2)=x-1`

`<=>3x-9-2x+4=x-1`

`<=>x-5=x-1`

`<=>-5=-1` 

Điều này vô lý 

`=>` Không có x thỏa mãn

Answer 2

\(\dfrac{3}{\left(x-1\right)\left(x-2\right)}-\dfrac{2}{\left(x-1\right)\left(x-3\right)}=\dfrac{1}{\left(x-2\right)\left(x-3\right)}\)`(ĐKXĐ x≠1  , 2 , 3)`

`=> BCNN: (x-1)(x-2)(x-3)`

`=> `\(\dfrac{3\left(x-3\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}-\dfrac{2\left(x-2\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}=\dfrac{x-1}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)

`=3(x-3) - 2(x-2) = x-1`

`=>3x - 9 -2x + 4 = x-1`

`=> 3x - 2x -x = 9 - 4 -1`

`=> x - x = 4`

`=> 0 = 4`(vô lý)

`=> x ∈∅`