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