Rút gọn biểu thức: C=(a^2−căna)/(a+căna+1)−(a^2+căna)/(a−căna+1)+a+1

* Hướng dẫn giải

$$\begin{gathered} \begin{array}{l}C=\frac{a^2-\sqrt{a}}{a+\sqrt{a}+1}-\frac{a^2+\sqrt{a}}{a-\sqrt{a}+1}+a+1(DK:a\ge 0)\\ C=\frac{\sqrt{a}\left[{\left(\sqrt{a}\right)}^3-1\right]}{a+\sqrt{a}+1}-\frac{\sqrt{a}\left[{\left(\sqrt{a}\right)}^3+1\right]}{a-\sqrt{a}+1}+a+1\end{array} \\ \begin{array}{l}=\sqrt{a}(\sqrt{a}-1)-\sqrt{a}(\sqrt{a}+1)+a+1\\ =a-\sqrt{a}-a-\sqrt{a}+a+1\\ ={\left(\sqrt{a}-1\right)}^2\end{array} \end{gathered}$$