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

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

(2x-8) (x-4) = 2x^2 - 16x - 32

(4x^2+8x+3) - (2x^2-16x-32) = 1

2x^2 - 8x - 29 = 1

2x^2 - 8x - 30 = 0

x^2 - 4x - 15 = 0

Using the quadratic formula;

x = 6.36 or x= -2.36 to 2dp