a: ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\a\ne1\end{matrix}\right.\)
b: \(Q=\left(\dfrac{1}{2+2\sqrt{a}}+\dfrac{1}{2-2\sqrt{a}}-\dfrac{a^2+1}{1-a^2}\right)\left(1+\dfrac{1}{a}\right)\)
\(=\left(\dfrac{1}{2\left(\sqrt{a}+1\right)}-\dfrac{1}{2\left(\sqrt{a}-1\right)}+\dfrac{a^2+1}{\left(a-1\right)\left(a+1\right)}\right)\cdot\dfrac{a+1}{a}\)
\(=\left(\dfrac{\sqrt{a}-1-\sqrt{a}-1}{2\left(a-1\right)}+\dfrac{a^2+1}{\left(a-1\right)\left(a+1\right)}\right)\cdot\dfrac{a+1}{a}\)
\(=\left(\dfrac{-2}{2\left(a-1\right)}+\dfrac{a^2+1}{\left(a-1\right)\left(a+1\right)}\right)\cdot\dfrac{a+1}{a}\)
\(=\left(-\dfrac{1}{a-1}+\dfrac{a^2+1}{\left(a-1\right)\left(a+1\right)}\right)\cdot\dfrac{a+1}{a}\)
\(=\dfrac{-a-1+a^2+1}{\left(a-1\right)\left(a+1\right)}\cdot\dfrac{a+1}{a}\)
\(=\dfrac{a^2-a}{a\left(a-1\right)}=1\)
