Khi rút gọn biểu thức \(\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\), ta được kết quả là
\(4a\). \(-4a\). \(a+1\). \(a-1\). Hướng dẫn giải:\(\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\)
\(=\left(\dfrac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+4\sqrt{a}\right)\left(\dfrac{a-1}{\sqrt{a}}\right)\)
\(=\left(\dfrac{a+2\sqrt{a}+1-\left(a-2\sqrt{a}+1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+4\sqrt{a}\right).\dfrac{a-1}{\sqrt{a}}\)
\(=\left(\dfrac{4\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+4\sqrt{a}\right).\dfrac{a-1}{\sqrt{a}}\)
\(=4\sqrt{a}\left(\dfrac{1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+1\right).\dfrac{a-1}{\sqrt{a}}\)
\(=4\left(\dfrac{1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right).\left(a-1\right)\)
\(=4\left[1+\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)\right]\)
\(=4a\)