\(\sqrt{1+\frac{1}{a^2}+\frac{1}{\left(a+1\right)^2}}=\sqrt{\left(1+\frac{1}{a}-\frac{1}{a+1}\right)^2}=\left|1+\frac{1}{a}-\frac{1}{a+1}\right|\)
Đây xem nhá
\(\sqrt{1+\frac{1}{a^2}+\frac{1}{\left(a+1\right)^2}}=\sqrt{\frac{\left(a\left(a+1\right)\right)^2+\left(a+1\right)^2+a^2}{a^2\left(a+1\right)^2}}=\sqrt{\frac{\left(a\left(a+1\right)\right)^2+a^2+2a+1+a^2}{a^2\left(a+1\right)^2}}=\sqrt{\frac{\left(a\left(a+1\right)\right)^2+2a\left(a+1\right)+1^2}{a^2\left(a+1\right)^2}}\)
\(=\sqrt{\left(\frac{a\left(a+1\right)+1}{a\left(a+1\right)}\right)^2}=\left|\frac{a\left(a+1\right)+1}{a\left(a+1\right)}\right|\)
