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Q: Explain the five-steps for solving rational equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier
to understand?
A: Step 1: Eliminate all fractions. When solving rational equations, you have a choice of two ways to eliminate the fractions. Option 1; multiply the entire problem by the least common denominator or LCD. Option 2; you can cross multiply. [ Option 1 will work for any problem, but you can only cross multiply if you have one fraction equal to one fraction, that is, if the fractions are proportional.
Click on the link to review the steps for Finding the LCD. Note that when solving rational equations all fractions should disappear after the first step. Step 2: Simplify the resulting equation. To simplify the equation you may need to distribute and combine like terms. Step 3: Solve the simplified equation. If the simplified equation has any higher powers such as x2 or x3, you can solve the equation by getting it equal to zero and factoring. If the simplified problem does not contain any higher powers, then solve for x by getting the x?s on one side and the numbers on the other. Step 4: Check each solution. Substitute each solution into the denominator of the original question and reject any solutions that cause the denominator to equal zero because this makes the problem undefined. This step does not guarantee that the answer is correct; it only guarantees that the answer is acceptable. ]
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