Simplify the rational expression.

To simplify a rational expression, start by factoring both the numerator and the denominator to their simplest forms. For example, if you have something like (x^2 - 4)/(x^2 - x - 6), you can factor the numerator as (x - 2)(x + 2) and the denominator as (x - 3)(x + 2). Here, you can cancel out the common factor of (x + 2), leaving you with (x - 2)/(x - 3). Simplification can make problems easier to handle—just remember to check for restrictions on your variable to avoid division by zero! Once you've simplified, always go back and verify your work. A common mistake is overlooking hidden factors or miscalculating during the factoring process. If you're unsure, substituting a few values into the original and simplified expressions can confirm that they yield the same results, which is a great way to spot any errors!