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.
Example 1
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Example 2
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Example 3
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Example 4
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Example 5
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