(2x+3)/(x-4) - (2x-8)/(2x+1) = 1 Solve for x

Multiply out the denominator, take care to multiply both sides of the equation:

(2x+3)(2x+1) - (2x-8)(x-4) = (2x+1)(x-4)

Expand the brackets, pay attention the the signs when multiplying, expecially the negative between the two sets of brackets on the left hand side.

4x²+2x+6x+3 - (2x²-8x-8x+32)=2x²-7x-4

4x²+2x+6x+3-2x²+8x+8x-32=2x²-7x-4

Group like terms on each side of the equation.

2x²+24x-29=2x²-7x-4

Bring all the terms to one side to leave a quadratic equation equal to 0. Remember to change the sign as you bring a term from one side to the other. 

31x-25 = 0

Rearrange for x

x= 25/31 (=0.81)