Please Simplify: (2x^2+3x/(2x+3)(x-2))-(6/x^2-x-2))

Factorise both parts of the question. Our left side would become x(2x+3)/(2x+3)(x-2) and our right side would become 6/(x+1)(x-2). On our LHS the (2x+3) would cancel leaving x/x-2. In order to merge the fraction together, the denominators need to be the same. You should multiply the LHS by (x+1). After doing this, the denominators will match and therefore you can merge them. After merging the two denominators you get x^2+x-6/(x-2)(x+1). If you factor the numerator you get (x-2)(x+3). Then, the (x-2) cancels out and you are left with (x+3)/(x+1)