|2x-3|=1/x
=> |2x-3| = \(\frac{1}{x}\)
=> TH1 :
2x-3=1/x
=> 2x=91/30
=> x=91/60
TH2 : 2x-3=-1/x
=> 2x=89/30
=> x=89/60
\(!2x-3!=\frac{1}{x}\)
DK:\(x>0\)
\(\left(1\right)2x-3=\frac{1}{x}\Leftrightarrow2x^2-3x-1=0\Leftrightarrow\left(4x-3\right)^{^2}-17=0\Rightarrow x=\frac{3-\sqrt{17}}{4}\left(loai\right);x=\frac{3+\sqrt{17}}{4}\)
\(\left(2\right)2x-3=-\frac{1}{x}\Leftrightarrow2x^2-3x+1=0\Rightarrow x=1\&x=\frac{1}{2}\)