How to solve 8/x^2-1=6/x+1

You first need to cross multiply to get 8x+8=6x^2-6. Then make the function into 6x^2-8x-14=0 which can be simplified into 3x^2-4x-7=0 by dividing the equation by 2. Then you must split the middle (-4x) to get 3x^2+3x-7x-7=0. This simplifies to 3x (x+1) - 7 (x+1) = 0 and then to (3x-7) (x+1) = 0. From here you just solve for each root which you will find are x = - 1 and 7/3