You may want to review simplifying rational functions first.

To solve a rational equation, you first get it into the form something = 0. Then you simplfy the something (which may be a complicated rational expression). Once it's simplified, a rational expression is 0 exactly where its numerator is 0, so you just set the numerator to 0 and solve for x. For example, you might need to solve (x + 3) / (x / (−2)) = 1. Moving everything to one side gives you (x + 3) / (x / (−2)) − 1 = 0. Simplifying the left-hand side gives you (−3x − 6) / x = 0. Now we need to solve the equation −3x − 6 = 0. We get x = −2, which is our answer.

There's one more thing we need to check, though. We need to put −2 back into the original equation, to make sure it doesn't create a division by 0. If it did, it wouldn't be a solution. (There would then be no solution.) It doesn't, though, so it is a solution.

As I mentioned above, rational equations don't always have solutions. Another way they can have no solution is if the numerator of the simplified left-hand side is a nonzero number. At the other extreme, if the equation simplifies to 0 = 0 then it's an identity.

If the numerator of the simplifies left-hand side is a polynomial of degree higher than 1, it might not be obvious how to solve it. In these problems, though, it will always be at most linear.