## anonymous one year ago Classify the solutions of 1 over x plus 4, plus one half, equals 1 over x plus 4 as extraneous or non-extraneous.

1. anonymous

Can you draw the equation, it is difficult to understand .

2. anonymous

|dw:1439570678077:dw|

3. anonymous

$\frac{ 1 }{ x+4 }+\frac{ 1 }{ 2 }=\frac{ 1 }{ x+4 }$

4. anonymous

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.

5. anonymous

x = -4; extraneous x = -4; non-extraneous x = -8; extraneous x = -8; non-extraneous

6. anonymous

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'