Question

cho M=\(\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{a-\sqrt{ }a}\right)\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{a-1}\right)\)với a>0

Answer 1

\(M=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{a-\sqrt{a}}\right)\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{a-1}\right)\)

     \(=\left[\dfrac{a}{\sqrt{a}\left(\sqrt{a}-1\right)}-\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right]\left[\dfrac{\sqrt{a}-1}{a-1}+\dfrac{2}{a-1}\right]\)

     \(=\dfrac{a-1}{\sqrt{a}\left(\sqrt{a}-1\right)}.\dfrac{\sqrt{a}-1}{a-1}\)

     \(=\dfrac{1}{\sqrt{a}}\)

Answer 2

\(M=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{a-\sqrt{a}}\right)\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{a-1}\right)\)

     \(=\left[\dfrac{a}{\sqrt{a}\left(\sqrt{a}-1\right)}-\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right]\left[\dfrac{\sqrt{a}-1}{a-1}+\dfrac{2}{a-1}\right]\)

     \(=\dfrac{a-1}{\sqrt{a}\left(\sqrt{a}-1\right)}.\dfrac{\sqrt{a}+1}{a-1}\)

     \(=\dfrac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}\)