A rational function, as the name implies, is a ratio of two polynomial functions. This means that we will be dealing with functions that have ratios, or fractions, in them.

In this unit we are learning how to solve rational equations. Although we know we can do this graphically (using a calculator and looking for the intersection of the two functions on either side of the equation), we will attempt to solve these algebraically. Solving rational equations algebraically will sometimes require us to factor quadratics as we've done before. As such, we will again need to use our factoring skills from previous units.

Once we have found our solutions, we will check them to see if any are "extraneous." Extraneous solutions are those that we get from algebraically solving the equation but in reality do NOT satisfy the original equation. Why does this happen? Because in the process of removing the fractions we changed the original equation so fundamentally that we lost some of the restrictions of the original function. The way we check for these "false" solutions is to plug our solutions back into the original equation and see if they really work. In these cases, an extraneous solution will be discovered whenever it forces us to divide by zero in a denominator of our original equation.