a, đk a >= 0 ; a khác 1
\(A=\left(\dfrac{a+\sqrt{a}+1}{a+1}\right):\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(a+1\right)}\right)\)
\(=\dfrac{a+\sqrt{a}+1}{a+1}:\dfrac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)\left(a+1\right)}=\dfrac{a+\sqrt{a}+1}{\sqrt{a}-1}\)
b, \(A-1=\dfrac{a+\sqrt{a}+1-\sqrt{a}+1}{\sqrt{a}-1}=\dfrac{a+2}{\sqrt{a}-1}< 0\Rightarrow\sqrt{a}-1< 0\Leftrightarrow a< 1\)
Kết hợp đk vậy 0 =< a < 1
c, \(a=\left(\sqrt{1994}-1\right)^2\Rightarrow\sqrt{a}=\sqrt{1994}-1\)
\(A=\dfrac{\left(\sqrt{a}+\dfrac{1}{2}\right)^2+\dfrac{3}{4}}{\sqrt{a}-1}=\dfrac{\left(\sqrt{1994}+\dfrac{1}{2}\right)^2+\dfrac{3}{4}}{\sqrt{1994}-2}=\dfrac{\left[\left(\sqrt{1994}+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\right]\left(\sqrt{1994}+2\right)}{1990}\)
