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Q: Why should you check your solutions after you solve rational expression?
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When solving a rational equation why is it necessary to perform a check?

It is important to check your answers to make sure that it doesn't give a zero denominator in the original equation. When we multiply both sides of an equation by the LCM the result might have solutions that are not solutions of the original equation. We have to check possible solutions in the original equation to make sure that the denominator does not equal zero. There is also the possibility that calculation errors were made in solving.


After you add or subtract two rational expressions its a good idea to see if you can your answer?

You should check whether you can simplify the answer.


What must you do to determine weather a soluion is an exraneous solution?

If the solution, makes the denominator equal to zero, makes the expression of a logarithm or under a square root, a negative one. If there are more than one denominator, check all the solutions. Usually, we determine the extraneous solutions before we solve the equation.


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Why is the sum of an rational number and irrational number an irrational number?

The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.


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What do you do to check whether a number is rational or irrational?

If its decimal representation is either terminating or a repeating number then it is rational. Otherwise it is irrational.


In general when solving a radical equation should you first isolate the radical and then both sides?

It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.


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How do you now if a fraction is rational?

It doesn't have a square root, or check mark symbol


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