solve to 2 decimal places; (2x+3/(x-4)) - 2x-8/(2x+1) = 1

the key to this question is to remove all the unknown denominators. to do this first move the negative fraction to the other side of the equation to get 2x+3/(x-4)=1 + 2x-8/(2x+1). then we need to combine the right hand side of the equation into 1 fraction. to do this turn 1 into 2x+1/2x+1, which isequialent to 1. then combine the two fractions on the right to get 2x+1+2x-8/(2x+1). this simplifies to 4x-7 over 2x+1. now bring back in the left hand side and times across by the denominators to get (2x+3)(2x+1)= (4x-7)(x-4). expand this to get 4xsquared + 6x +2x +3 = 4xsquared - 16x - 7x +28. this simplies to 31x = 25 and this equals 0.81 to 2 dp.