Question

\(\dfrac{\sqrt{x^4-4x^2+4}}{x^2-2}\)

Answer 1

\(=\dfrac{\sqrt{\left(x^2-2\right)^2}}{x^2-2}=\dfrac{x^2-2}{x^2-2}=1\)

Answer 2

`\sqrt{x^4-4x^2+4}/[x^2-2]`          `ĐK: x \ne \sqrt{2}`

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

`=[|x^2-2|]/[x^2-2]`

`@` Với `x^2-2 > 0=>|x^2-2|=x^2-2`

   `=>\sqrt{x^4-4x^2+4}/[x^2-2]=[x^2-2]/[x^2-2]=1`

`@` Với `x^2-2 < 0=>|x^2-2|=-(x^2-2)`

   `=>\sqrt{x^4-4x^2+4}/[x^2-2]=[-(x^2-2)]/[x^2-2]=-1`

Answer 3