Question

Answer 1

1: ĐKXĐ: a>=0; a<>1

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

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

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

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

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

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

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