Question 199891: explain why clearing the fraction to simplify a rational inequality may lead to a false solution
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! usually extraneous solution arise when we are working with squares or square roots
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it is reasonable that sqrt of 4 = +/- 2
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however if the solution is someone's age, the -2 answer is not reasonable
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Likewise if we square x to x^2, and later have to take a sqrtx^2 = +/- x,,,,,,
sometimes the minus answer is not reasonable. However, we must check to assure we do not discard a reasonable answer.
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It is always good to check all answers, but as the math gets more complicated, it is very important to check. With practice it become easier.
Good Luck and keep up the good work
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