Bài 1:
\(A=\left(\dfrac{m+\sqrt{m^2-n^2}}{m-\sqrt{m^2-n^2}}-\dfrac{m-\sqrt{m^2-n^2}}{m+\sqrt{m^2-n^2}}\right):\dfrac{4m\sqrt{m^2-n^2}}{n^2}\)
\(A=\left[\dfrac{\left(m+\sqrt{m^2-n^2}\right)^2}{\left(m-\sqrt{m^2-n^2}\right)\left(m+\sqrt{m^2-n^2}\right)}-\dfrac{\left(m-\sqrt{m^2-n^2}\right)^2}{\left(m-\sqrt{m^2-n^2}\right)\left(m+\sqrt{m^2-n^2}\right)}\right]:\dfrac{4m\sqrt{m^2-n^2}}{n^2}\)
\(A=\dfrac{\left(m+\sqrt{m^2-n^2}\right)^2-\left(m-\sqrt{m^2-n^2}\right)^2}{\left(m-\sqrt{m^2-n^2}\right)\left(m+\sqrt{m^2-n^2}\right)}\cdot\dfrac{n^2}{4m\sqrt{m^2-n^2}}\)
\(A=\dfrac{\left(m+\sqrt{m^2-n^2}+m+\sqrt{m^2-n^2}\right)\left(m+\sqrt{m^2-n^2}-m+\sqrt{m^2-n^2}\right)}{m^2-\left(\sqrt{m^2-n^2}\right)^2}\cdot\dfrac{n^2}{4m\sqrt{m^2-n^2}}\)
\(A=\dfrac{2m\cdot2\sqrt{m^2-n^2}}{m^2-m^2+n^2}\cdot\dfrac{n^2}{4m\sqrt{m^2-n^2}}\)
\(A=\dfrac{4m\sqrt{m^2-n^2}}{n^2}\cdot\dfrac{n^2}{4m\sqrt{m^2-n^2}}\)
\(A=\dfrac{4mn^2}{4mn^2}\)
\(A=1\)
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