2((x+ 1/x)? -2)-3(x+ 1/x)- 1=0
2(x+ 1/x)? -3(x+ 1/x)-5=0
Let x+1/x = y.
rule
2y? -3y-5=0
(y+ 1)(2y-5)=0
Y=- 1 or y=5/2.
rule
x+ 1/x=- 1
x? +x+ 1=0, no solution.
Or x+ 1/x=5/2.
That's 2x? -5x+2=0
(2x- 1)(x-2)=0
Get X= 1/2 or x=2.
To sum up, the solution of the equation is x= 1/2 or x=2.