ĐK: `a \ne 1, a>0`
`L=((\sqrta-2)/(a-1)-(\sqrta+2)/(a+2\sqrta+1))(1+1/(\sqrta))`
`=( (\sqrta-2)/((\sqrta+1)(\sqrta-1)) - (\sqrta+2)/((\sqrta+1)^2)) ( (\sqrta+1)/(\sqrta))`
`=((\sqrta-2)(\sqrta+1)-(\sqrta+2)(\sqrta-1))/((\sqrta-1)(\sqrta+1)^2) . (\sqrta+1)/(\sqrta)`
`= (-2\sqrta)/(\sqrta(a-1))`
`=(-2)/(a-1)`
Ta có: \(L=\left(\dfrac{\sqrt{a}-2}{a-1}-\dfrac{\sqrt{a}+2}{a+2\sqrt{a}+1}\right)\left(1+\dfrac{1}{\sqrt{a}}\right)\)
\(=\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+1\right)-\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}+1\right)^2\cdot\left(\sqrt{a}-1\right)}\cdot\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
\(=\dfrac{a-\sqrt{a}-2-a-\sqrt{a}+2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)\cdot\sqrt{a}}\)
\(=\dfrac{-2}{a-1}\)
