\(C=\left(1-\dfrac{2\sqrt{a}}{a+1}\right)\left(\dfrac{1}{\sqrt{a}+1}-\dfrac{2\sqrt{a}}{a\sqrt{a}+\sqrt{a}+a+1}\right)\) (ĐK: a > 0)
\(=\left(\dfrac{a+1-2\sqrt{a}}{a+1}\right)\left[\dfrac{a+1}{\left(\sqrt{a}+1\right)\left(a+1\right)}-\dfrac{2\sqrt{a}}{\sqrt{a}\left(a+1\right)+\left(a+1\right)}\right]\)
\(=\dfrac{\left(\sqrt{a}-1\right)^2}{a+1}\cdot\left[\dfrac{a+1}{\left(\sqrt{a}+1\right)\left(a+1\right)}-\dfrac{2\sqrt{a}}{\left(\sqrt{a}+1\right)\left(a+1\right)}\right]\)
\(=\dfrac{\left(\sqrt{a}-1\right)^2}{a+1}\cdot\dfrac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(a+1\right)}\)
\(=\dfrac{\left(\sqrt{a}-1\right)^4}{\left(\sqrt{a}+1\right)\left(a+1\right)^2}\)
#Ayumu
