But wait, there's more. Solutions. How do we solve these bad boys?
A rational equation is an equation with at least one rational expression all up in it. That means fractions. To solve a rational equation for x (or whatever variable), we need to get rid of those beastly fractions. Here's how.
- Find the LCM of all the denominators.
- Multiply each term of the equation by the LCM.
- Solve just like you would with a linear or quadratic equation.
Not too bad. (For a refresher on what linear and quadratic equations are, check here and here.)
Any solutions that cause a denominator to be zero in the original equation are dirty, dirty liars. They're not really solutions at all. They should not pass "Go," nor should they collect $200. Anytime we multiply by a variable or square a variable, we've got to check our solutions. Probably the easiest way to do this is by checking to see if our solutions are within our domain—which brings us to our next topic.