solve for x -   2(2x-1/x+3)-3(x+3/2x-1)=5

Let (2x-1/x+3) = y   (then, (x+3/2x-1) = 1/y)

Then, the given equation becomes:

2y - 3 / y = 5

or, 2y² - 3 = 5y

or, 2y² - 5y - 3 = 5y

or, 2y² - 5y - 3 = 0

( 2y² - 5y - 3 = 5y)

or, 2y² - 6y + y - 3 = 0

or, 2y(y-3) + 1(y-3) = 0

or, (y - 3)(2y + 1) = 0

Therefore,  y = 3 or  y = -1/2

Now, (2x-1/x+3) = y = 3

=> (2x-1) / (x+3) = 3

=> 2x - 1 = 3x + 9

=> x + 10 = 0

=> x = -10.

Also, (2x-1/x+3) = y = -1/2

=> (2x-1) / (x+3) = -1/2

=> 2x -1 = (-x-3) / 2

=> 4x - 2 = -x-3

=> 5x + 5 = 0

=> x = -1.

So, the solutions of the given equation are -10 and -1.

sry., 

(=> 4x - 2 = -x-3

=> 5x + 5 = 0  X  wrong

=> x = -1.  X  wrong

So, the solutions of the given equation are -10 and -1.) 

Also, (2x-1/x+3) = y = -1/2

=> (2x-1) / (x+3) = -1/2

=> 2x -1 = (-x-3) / 2

=> 4x - 2 = -x-3

=> 5x + 1 = 0

=> x = -1/5

So, the solutions of the given equation are -10 and -1/5.

answer: 

let y=(2x+3/x-3) & 1/y=(x-3/2x+3)

substuting the values.. 

2y^2 -25/y=5

• 2y^2-25=5y
• 2y^2-5y-25=0
• 2y^2-10y+5y-25=0
• 2y(y-5)+5(y-5)=0
• y=5 or y=-5/2
• when y=5
• 2x+3/x+3=5
• 2x+3=5x-15
• -3x=-18x
• x=6

when y=-5/2

2x+3/x-3=-5/2

4x+6=-5x+15

9x=15-6

x=1