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 (−3*x* − 6) / *x* = 0. Now we
need to solve the equation −3*x* − 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.