Question

Answer 1

1: 

ĐKXĐ: a>=0; a<>1

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

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

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

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

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

2: Để A<1/3 thì A-1/3<0

\(\Leftrightarrow\dfrac{a}{a+1}-\dfrac{1}{3}< 0\)

\(\Leftrightarrow\dfrac{3a-a-1}{3\left(a+1\right)}< 0\)

=>2a-1<0

hay 0<a<1/2