\(ĐK:x\ne0;x\ne1\)
\(\Leftrightarrow\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\sqrt{x}+1}{\sqrt{x}}\)
\(\Leftrightarrow\frac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}-\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(\Rightarrow x-1=x^2-1\)
\(\Leftrightarrow-x^2+x=0\)
⇔ x( -x + 1 ) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\-x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=1\left(ktm\right)\end{matrix}\right.\)
Vậy tập nghiệm của pt là : \(S=\phi\)
đkxđ x#1 và x#0
xét VT= \(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
= \(\frac{x-1}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\left(\sqrt{x}+1\right)}{\sqrt{x}}=VP\left(đpcm\right)\)
