To add and subtract rational expressions, it is easiest to start with a common denominator. This can be found by factoring.

With this example

There needs to be a common denominator, so we can find what they both need or have in common. Since this is a binomial denominator, we can leave them in the factored forms.

We can then put all the numerator terms together to create one big fraction

Once the expression is simplified, we can go back to find the non-permissible values.

To do this, we can look at the original expression and find the number that, if replaced x, would result in a 0. If x = 2 and 2 is subtracted, that is 0, which is not allowed to be the numerator. If x is -2 and 2 is added, it becomes a 0. The non-permissible values for x are -2, 2