A* grade question: ((2x+3)/(x-4))-((2x-8)/(2x+1))=1 solve for X

Multiply whole equation by x-4 and then 2x+1 (would do this one step at a time but must conserve space here):

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

Expand brackets:

(4x^2+8x+3)-(2x^2-16x+32)= 2x^2-7x-4

Do the subtraction: 2x^2+24x-29=2x^2-7x-4

Minus 2x^2 from both sides:

24x-29=-7x-4

Bring Xs to left hand side and integers to right hand side of equals sign:

31x=25

X=25/31