Express 3/2x+3 – 1/2x-3 + 6/4x^2-9 as a single fraction in its simplest form.

First it is necessary to notice that 4x^2-9 can be written as (2x-3)(2x+3). To solve this question, you first have to write all the fractions in terms of their lowest common denominator. In this case that is (2x+3)(2x-3). Therefore you have to multiply 3/2x+3 by 2x-3/2x-3 and 1/2x-3 by 2x+3/2x+3. This will leave you with 3(2x-3)-1(2x+3)+6/(2x-3)(2x+3). If you multiply this out you are left with 4x-6/(2x-3)(2x+3). 4x-6 can be rewritten as 2(2x-3), and therefore the 2x-3s cancel out leaving 2/2x+3 which is the final answer.