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Rational equation, Rational expression, Quadratic equations

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1. When solving a rational equation, why it is ok to remove the denominator by multiplying both sides by the LCD (least common denominator)? Why can you not do the same operation when simplifying a rational expression?
2. Why are there usually two solutions in quadratic equations? Under what situation would one or more solutions of a rational equation be unacceptable?
3. What square root property is essential to solve any radical equation involving radicals?

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The expert examines rational equations for the least common denominator. A complete, neat and step-by-step solution is provided in the attached file.

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1. When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression?
2. Why are there usually two solutions in quadratic equations? Under what situation would one or more solutions of a rational equation be unacceptable?
3. What square root property is essential to solve any radical equation involving radicals?
(1) As a rule, we can ...

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