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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Can you draw the equation, it is difficult to understand .
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\[\frac{ 1 }{ x+4 }+\frac{ 1 }{ 2 }=\frac{ 1 }{ x+4 }\]

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Other answers:

if you subtract 1/(x+4) from both sides, you get 1/2 = 0, which is a contradiction. There are no solutions to this equation.
x = -4; extraneous x = -4; non-extraneous x = -8; extraneous x = -8; non-extraneous
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If you solve the equation $$ \frac{1}{(x+4)} + \frac 1 2 = \frac{ 1}{(x+4)} \\ \ \\ \frac{2}{2(x+4)} + \frac {(x+4)}{2(x+4)} = \frac{ 1}{(x+4)} \\ \ \\ \frac{2+ (x+4) }{2(x+4)} = \frac{ 1}{(x+4)} \\ \ \\ \frac{x+6 }{2(x+4)} = \frac{ 1}{(x+4)} \\ \ \\ x + 6 = \frac{ 1}{(x+4)} \cdot 2(x+4) \\ \ \\ x + 6 = 2 \\ \\ x = -4 $$ But -4 does not satisfy original equation. Hence we say -4 is 'extraneous'

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