Classify the solutions of 1 over x plus 4, plus one half, equals 1 over x plus 4 as extraneous or non-extraneous

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Classify the solutions of 1 over x plus 4, plus one half, equals 1 over x plus 4 as extraneous or non-extraneous

Mathematics
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lol there is either a solution, or there is not not sur what math teacher made up this "extraneous' nonsense
\[\frac{1}{x+4}+\frac{1}{2}=\frac{1}{x+4}\]? is that the question?
i just need help with the extraneous and non extraneous

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yes that is
a bit hard to read
oh ok then lets think
x is a variable, it can be anything but whatever it is on the left, it is the same on the right so if you add one half to a number, it is impossible to get the same number back there is NO SOLUTION
the answer is x= -4 but idk if its extraneous or not
THE ANSWER IS NOT X = -4
then what is it? bc i followed the directions in the lesson
ok fine, say \(x=-4\) is "extraneous" if that will make your math teacher happy
do you know the difference between the two?
\[\overbrace{\frac{1}{x+4}}^{\text{this}}+\frac{1}{2}=\overbrace{\frac{1}{x+4}}^{\text{is equal to this}}\]
ok
you cannot add one half to a number and get the same number back
the not very bright math teacher who wants you not to think like a person, but do some steps to "solve" wants you to find that \(x=-4\) but \(x\) cannot be \(-4\) because a) that would make the denominator zero and b) there is NO SOLUTION
therefore they want you to behave like a robot and say "the solution is \(x=-4\) but it is "extraneous""
x = −4; extraneous x = −4; non-extraneous x = −8; extraneous x = −8; non-extraneous so out of these answer choices......its the first one?

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