\(C=\dfrac{a^2-3a-\left(a-1\right)\sqrt{a^2-4}+2}{a^2+3a-\left(a+1\right)\sqrt{a^2-4}+2}.\sqrt{\dfrac{a+2}{a-2}}\)
\(\Leftrightarrow\dfrac{a^2-3a+\left(-a+1\right)\sqrt{a^2-4}+2}{a^2+3a+\left(-a-1\right)\sqrt{a^2-4}+2}.\sqrt{\dfrac{a+2}{a-2}}\)
\(\Leftrightarrow\)\(\dfrac{\left[a^2-3a+\left(-a+1\right)\sqrt{a^2-4}+2\right]\sqrt{a+2}}{\left[a^2+3a+\left(-a-1\right)\sqrt{a^2-4}+2\right]\sqrt{a-2}}\)
\(\Leftrightarrow\)\(\dfrac{a^2\sqrt{a+2}-3a\sqrt{a+2}+\left(-a+1\right)\sqrt{a^2-4}\sqrt{a+2}+2\sqrt{a+2}}{a^2\sqrt{a-2}+3a\sqrt{a-2}+\left(-a-1\right)\sqrt{a^2-4}\sqrt{a-2}+2\sqrt{a-2}}\)
\(\Leftrightarrow\)\(\dfrac{a^2\sqrt{a+2}-3a\sqrt{a+2}+\left(-a+1\right)\sqrt{a^3+2a^2-4a-8}+2\sqrt{a+2}}{a^2\sqrt{a-2}+3a\sqrt{a-2}+\left(-a-1\right)\sqrt{a^3-2a^2-4a+8}+2\sqrt{a-2}}\)
