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.