Question

[Nguyễn Quỳnh Chi]

Mng cứu em bài này với ạaa

Rút gọn

^{\(\dfrac{x^2-\sqrt{2}}{x^4+\left(\sqrt{3}-\sqrt{2}\right)\cdot x^2-\sqrt{6}}\)}

Answer 1

[Xyz OLM]

ĐKXĐ : \(x^4+\left(\sqrt{3}-\sqrt{2}\right).x^2-\sqrt{6}\ne0\)

\(\Leftrightarrow x\ne\sqrt[4]{2}\)

\(P=\dfrac{x^2-\sqrt{2}}{x^4+\left(\sqrt{3}-\sqrt{2}\right).x^2-\sqrt{6}}\)

\(=\dfrac{x^2-\sqrt{2}}{\left(x^4-\sqrt{2}x^2\right)+\sqrt{3}\left(x^2-\sqrt{2}\right)}\) 

\(=\dfrac{x^2-\sqrt{2}}{\left(x^2+\sqrt{3}\right)\left(x^2-\sqrt{2}\right)}=\dfrac{1}{x^2+\sqrt{3}}\)