How to solve the following for x: (2x+3)/(x-4) - (2x-8)(2x+1) = 1

(The full answer produced answer is annotated working out, but since this text box won't let me submit pictures, I'll do my best to transcribe)First, we gather the two fractions by using a common denominator:[(2x + 3)(2x+1) - (2x-8)(x-4)] / [(x-4)(2x+1)] = 1Then, we can multiply both sides of the equation by the common denominator to avoid having to deal with a fraction:(2x + 3)(2x+1) - (2x-8)(x-4) = (x-4)(2x+1)Expanding out the brackets allows us to gather like terms and simplify:4x^2 + 2x + 6x + 3 - [ 2x^2 - 8x - 8x + 32 ] = 2x^2 + x - 8x - 4with a second line of working:24x - 29 = -7x - 4and a third:31x = 25And so dividing both sides by 31 gives us a final answer of x = 25/31