Mathematics » Rational Expressions and Equations » Solve Rational Equations

Defining Rational Equations

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.

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

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