First eliminate fractions;
Multiplying both sides by (x-4) gives;
(2x+3)-((2x-8)(x-4))/(2x+1)=(x-4)
Multiplying both sides by (2x+1) gives;
(2x+3)(2x+1)-(2x-8)(x-4)=(x-4)(2x+1)
Now simplify the expression;
Expanding the brackets gives;
(4x2+2x+6x+3)-(2x2-8x-8x+32)=(2x2+x-8x-4)
2x2+24x-29=2x2-7x-4
Subtract (2x2-7x-4) from both sides;
31x-25=0
Rearrange for x;
31x=25
x=25/31