a. \(A=\frac{2a^2+4}{1-a^2}-\frac{1}{1+\sqrt{a}}-\frac{1}{1-\sqrt{a}}\left(đkxđ:a\ge0;a\ne1\right)\)
\(=\frac{2a^2+4}{\left(1-a\right)\left(1+a\right)}-\frac{1}{1+\sqrt{a}}-\frac{1}{1-\sqrt{a}}\)
\(=\frac{2a^2+4}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a\right)}-\frac{\left(1-\sqrt{a}\right)\left(1+a\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a\right)}-\frac{\left(1+\sqrt{a}\right)\left(1+a\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a\right)}\)
\(=\frac{2a^2+4-\left(1+a-\sqrt{a}-a\sqrt{a}\right)-\left(1+a+\sqrt{a}+a\sqrt{a}\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a\right)}\)
\(=\frac{2a^2+4-1-a+\sqrt{a}+a\sqrt{a}-1-a-\sqrt{a}-a\sqrt{a}}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a\right)}\)
\(=\frac{2a^2-2a+2}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a\right)}=\frac{2a^2-2a+2}{1-a^2}\)
(mk chỉ rút gọn được đến đây thôi, có gì sai bạn tự sửa nha)
