Solve (6/x-2)-(2/x+3)=1

Firstly, begin by multiplying both sides of the equation by (x-2) and (x+3), this gives 6(x+3)-2(x-2)=(x+3)(x-2). Expand out the brackets on each side of the equation to give 6x+18-2x+4=x²-2x+3x-6. Next, equal the left side to 0 and simplify to achieve x²-3x-28=0. Find x by either substituting into the quadratic equation, or by factorising to provide the equation (x-7)(x+4)=0 and equalising x to 0. This gives the answer x=7 or x=-4