\(A^2=\frac{a^2\left(a+1\right)^2+\left(a+1\right)^2+a^2}{a^2\left(a+1\right)^2}\)
\(\Leftrightarrow A^2=\frac{\left(a+1\right)^2+a^2\left(a^2+2a+2\right)}{a^2\left(a+1\right)^2}\)
\(\Leftrightarrow A^2=\frac{\left(a+1\right)^2+2\left(a+1\right)a^2+a^4}{a^2\left(a+1\right)^2}\)
\(\Leftrightarrow A^2=\frac{\left(a+1+a^2\right)^2}{a^2\left(a+1\right)^2}\)
\(A=\sqrt{1+\frac{1}{a^2}+\frac{1}{\left(a+1\right)^2}}=\sqrt{\left(1+\frac{1}{a}\right)^2+\frac{1}{\left(a+1\right)^2}-\frac{2}{a}}\)
\(=\sqrt{\left(\frac{a+1}{a}\right)^2+\frac{1}{\left(a+1\right)^2}-\frac{2\left(a+1\right)}{a}\cdot\frac{1}{a+1}}\)
\(=\sqrt{\left(\frac{a+1}{a}-\frac{1}{a+1}\right)^2}=\left|\frac{1}{a}+1-\frac{1}{a+b}\right|\)
chỗ giá trị tuyệt đối cuối cùng sửa b thành 1 nhé gõ lộn
