Question 79742
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What is an extraneous solutions?

It's a "phony" solution that you get sometimes,
Even though you haven't made a mistake at all, it 
does not check when substituted into the original
equation. 

Tutor Paul above gave an example of a radical 
equation which has an extraneous solution. However,
when you study extraneous solutions for the first 
time, most likely you haven't studied radical 
equations yet, but only rational equations.  So
I think these examples would be more in line
with what you are studying in school.  I'm
guessing Paul's examples above are more
advanced that where you are in the course at the
present time, so I give these 2 examples:  

Example 1:

{{{3/(x-1) + 1/(x+1) = 6/(x^2-1)}}}

When you clear of fractions and solve the
equation, you get the "solution" x = 1 
However x = 1 does not check because it 
results in a denominator being 0, which 
is undefined.  So the equation has no
solution at all! x = 1 is called an
EXTRANEOUS solution, which is really
not a solution at all.

Example 2:

{{{x/(x-2)-4/(x+1) = 6/(x^2-x-2)}}}

When you multiply through by the LCD
and solve the resulting quadratic
equation, you get solutions x=2 and
x=1. However when we try to check the
solution x=2, it causes the first 
and last denominators to become 0, which
is undefined.  However x=1 checks.  So
we discard the extraneous solution x=2
and keep the x=1 as the only solution.

Edwin</pre>