## What are rational equations?

After defining the terms *expression* and *equation* early in this tutorial, we have used them throughout this book. We have *simplified* many kinds of *expressions* and *solved* many kinds of *equations*. We have simplified many rational expressions so far in this tutorial. Now we will solve rational equations.

The definition of a rational equation is similar to the definition of equation we used in this tutorial.

### Rational Equation

A **rational equation** is two rational expressions connected by an equal sign.

You must make sure to know the difference between rational expressions and rational equations. The equation contains an equal sign.

\(\begin{array}{cccc}\hfill \mathbf{\text{Rational Expression}}\hfill & & & \hfill \phantom{\rule{5em}{0ex}}\mathbf{\text{Rational Equation}}\hfill \\ \hfill \phantom{\rule{1.95em}{0ex}}\frac{1}{8}x+\frac{1}{2}\hfill & & & \hfill \phantom{\rule{3.1em}{0ex}}\frac{1}{8}x+\frac{1}{2}=\frac{1}{4}\hfill \\ \hfill \phantom{\rule{2.5em}{0ex}}\frac{y+6}{{y}^{2}-36}\hfill & & & \hfill \phantom{\rule{4.65em}{0ex}}\frac{y+6}{{y}^{2}-36}=y+1\hfill \\ \hfill \phantom{\rule{2.5em}{0ex}}\frac{1}{n-3}+\frac{1}{n+4}\hfill & & & \hfill \phantom{\rule{5em}{0ex}}\frac{1}{n-3}+\frac{1}{n+4}=\frac{15}{{n}^{2}+n-12}\hfill \end{array}\)