- What is a Rational Equation?
- A rational equation is an equation that contains at least one rational expression.
- To Solve a Rational Equation......
- Determine the lowest common denominator of all rational expressions in the equation.
- Multiply both sides of the equation by the lowest common denominator.
- Simplify by removing parentheses and combining like terms.
- Solve the equation resulting from step 4.
- Check the solution in the original equation. This step is essential since it is here that you will eliminate extraneous solutions (see below).
- What are Extraneous Solutions?
- An extraneous solution is a value that you think is a solution because it was found by the solving process but, this value does not solve the original equation.
- The way that you determine that a value is an extraneous solution is by checking that value in the original equation:
- If a value that you think is a solution does not solve the original equation,
then that value is an extraneous solution.
- The check step is where extraneous solutions are found.
- Always check all solutions in the original equation to make sure they solve the original equation.
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