I chose to do this because it is one of the more challenging things to do, so explaining it will help me learn more.

Algebraic fractions basically just means the fractions have variables. The rules don’t exactly change, but more are added on (exponent laws, factoring, simplifying, restrictions).

There are a few more things to watch out for, like opposites always cancelling out to -1 and binomials sometimes being the LCMs, though same rules apply.

You can see that (x+5) is the LCM, so it will be cancelled out anyway, meaning we can ignore it and write it once in our denominator.

To make a common denominator, we will need to multiply both sides by what will give them the common denominator, which is (x-3) on the left and (x-2) on the right

Now we can subtract

Note the minus sign in the middle, which will flip the signs of the fraction to the right.

In this fraction, we can see the the denominators can be factored.

Again, we have an LCM of (x+1)