How to express (4x)/(x^2-9)-2/(x+3)as a single fraction in its simplest form.

First we should be aware of the relationship bewteen the denominator of the two fractions. Since x^2-9=(x+3)(x-3), we can multiply (x-3) on both numerator and denominator of the fraction of 2/(x+3). Hence the fraction becomes 2(x-3)/(x+3)(x-3)=2(x-3)/(x^2-9). Therefore now we can substract it from the first fraction, becomes (4x)/(x^2-9)-2(x-3)/(x^2-9). Since the denominator is the same, so we can substact the numerator straightaway. And the next step will be [4x-2(x-3)]/(x^2-9)=(2x-6)/(x^2-9)=2(x-3)/(x^2-9). Be aware here that (x^2-9) can be split into (x+3)(x-3). This is a very common mistake. Hence devide (x-3) from both denominator and numerator and final answer will be 2/x+3.