Question 894272
Not sure if you mean exactly as written, but  LCD is 2x...


{{{2x(x-1/x)=(3/2)*2x}}}
{{{2x^2-2=3x}}}
{{{2x^2-3x-2=0}}}


According to general solution,
{{{x=(3+- sqrt(9+4*2*2))/(2*2)}}}
{{{x=(3+- sqrt(25))/4}}}
{{{x=(3+- 5)/4}}}
{{{highlight(x=-1/2)}}}  or  {{{highlight(x=2)}}}