Lời giải:
a.
ĐKXĐ: $x\geq 0; x\neq 1$
\(A=\frac{x\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}-\frac{(x-1)(\sqrt{x}-1)}{(\sqrt{x}+1)(\sqrt{x}-1)}=\frac{x\sqrt{x}+1-(x-1)(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\)
\(=\frac{x+\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}=\frac{\sqrt{x}(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}=\frac{\sqrt{x}}{\sqrt{x}-1}\)
b.
$A<1\Leftrightarrow \frac{\sqrt{x}}{\sqrt{x}-1}-1<0$
$\Leftrightarrow \frac{1}{\sqrt{x}-1}< 0$
$\Leftrightarrow \sqrt{x}-1<0$
$\Leftrightarrow 0< x< 1$
Kết hợp đkxđ suy ra $0<x<1$