Đặt biểu thức trên là N, ta có:
\(N=\frac{a^3-3a+\left(a^2-1\right)\sqrt{a^2-4}-2}{a^3-3a+\left(a^2-1\right)\sqrt{a^2-4}+2}\left(a\ge2\right)\)
\(\Leftrightarrow N=\frac{\left(a^3-3a-2\right)+\left(a^2+1\right)\sqrt{a^2-4}}{\left(a^3-3a+2\right)+\left(a^2+1\right)\sqrt{a^2-4}}\)
\(\Leftrightarrow N=\frac{\left(a-2\right)\left(a+1\right)^2+\left(a-1\right)\left(a+1\right)\sqrt{a^2-4}}{\left(a+2\right)\left(a-1\right)^2+\left(a-1\right)\left(a+1\right)\sqrt{a^2-4}}\)
\(\Leftrightarrow N=\frac{\sqrt{a-2}\left(a+1\right)\left[\sqrt{a-2}\left(a+1\right)+\left(a-1\right)\sqrt{a+2}\right]}{\sqrt{a+2}\left(a-1\right)\left[\sqrt{a+2}\left(a-1\right)+\left(a+1\right)\sqrt{a-2}\right]}\)
\(\Leftrightarrow N=\frac{\sqrt{a-2}\left(a+1\right)}{\sqrt{a+2}\left(a-1\right)}\)
(Chúc bạn học tốt và nhớ tíck cho mình với nhá!)