Step 1: Multiply everything by x-4 to give
(2x+3) - ((2x-8)(x-4)/2x+1)=(x-4)
Step2: Multiply everything by 2x+1 to give
(2x+3)(2x+1)-(2x-8)(x-4)=(x-4)(2x+1)
Step 3: Multiply out the brackets to give
(4x2+8x+3)-(2x2-16x+32)=2x2-7x-4
Step 4: Simplify to get a zero on one side of the equation to give
31x-25=0
Step 5: We therefore know that 31x = 25 so to find x divide 25 by 31 to get x=0.81 to 2 decimal places