Express 4x/(x^2-9) - 2/(x+3) as a single fraction in its simplest form.
In order to add or subtract terms to/from each other, both of their denominators (the number on the bottom of the fraction) must be the same. In this case they are different, so the first step is to try and simplify the bottom terms to see if there are any common factors.Straight away we should see that the LHS denominator (x2 - 9) is a difference of two squares, therefore can be simplified to (x+3)(x-3). Luckily, we can now identify that (x+3) is common in both terms. Now the next step is to make both denominators equal, by multiplying both top and bottom of the RHS fraction by (x-3), which allows us to combine the two terms under the same common denominator. Now, subtracting the terms yields (2x-6)/(x+3)(x-3), which can be further simplified to 2/(x+3) by dividing both both top and bottom by (x-3).
