Solving rational equations follows the same rules as solving any other type of equation. Whatever you do to one side
of the equation, you must do to the other. If you have fractions, you try to eliminate them by multiplying by the common denominator. If there are quadratics involved, you must get all terms to one side
with zero on the other. If you need practice solving linear equations (link to linear equations
) or solving quadratic equations
, click on the link to review those skills before working with rational equations.
Recall that a rational expression
is in the form of a fraction
where there is a variable
in the denominator. Solving rational equations will involve simplifying rational expressions. If you need to review that topic, click here
Before we begin with a rational function, let’s look at how we would handle an equation
Our first step in solving this equation
would be to multiply each term by the least common denominator of the fractions, which is 12.
Simplifying this particular equation
results in the following linear equation
which we can then solve to get our final answer.
It was important to look at an equation
that did not have a variable
in the denominator to make sure we see the pattern
for solving rational equations. Here are the steps we will use in our solution
- Determine the least common denominator of all the fractions in the equation.
- Eliminate the fraction(s) by multiplying ALL terms by the least common denominator.
- Simplify the terms.
- Solve the resulting equation.
- Check your answers to make sure the solution does not make the fraction undefined.