If (2x+3)/(x-4)-(2x-8)/(2x+1)=1, what is x?

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