How can I check my work on product of rational expressions?

Question

When solving a linear system of equations, it's easy to plug the solution back into the original equations to confirm that it's actually a solution. Is there a way to do check your work when multiplying rational expressions?

Answer 1

Yes: pick a random value for $x$ (assuming that's the variable), and evaluate both the original rational expression and the final one. If the results agree, chances are very good that the two expressions are equal. I recommend choosing something for $x$ that you very much think is not involved in the answer (esp. if it's a textbook problem). That means that $x = 0, 1, -1$ are all BAD choices, and $x = 2.4$ is a good one. ;)