SOLUTION: POST A 50 WORD RESPONSE TO THE FOLLOWING; WHEN SOLVING A RATIONAL EQUATION, WHY IS IT NECESSARY TO PERFORM A CHECK

Question 333521: POST A 50 WORD RESPONSE TO THE FOLLOWING; WHEN SOLVING A RATIONAL EQUATION, WHY IS IT NECESSARY TO PERFORM A CHECK
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
Wne solving rational equations, we always have to clear of fractions
which involves multiplying through by an LCD which is a variable expression.
But it is possible that that variable LCD that we multiplied through by
could equal zero. If that were the case then we would have made a violation
of multiplying through an equation by zero.
Take this case:

If we multiply through by the LCD = , we are assuming
that x is not equal to either 7 or 3. For it x were equal to either
7 or 3 then two of those denominators would be 0.
So we go ahead and multiply through by the LCD and get:

But in this case x would have to have equaled to 7.
That means we were in violation of multiplying through by 0.
So we got an extraneous solution, which is not a solution at all.
We discover this by substituting in the original equation:

That is meaningless because 0 in the denominator is not defined.
Edwin
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