# How do you solve x/(x+4)=2/x and check for extraneous solutions?

Apr 9, 2017

$x \in \left\{4 , - 2\right\}$

#### Explanation:

Multiply both sides.

$\frac{x}{x + 4} \cdot x \left(x + 4\right) = \frac{2}{x} \cdot x \left(x + 4\right)$

${x}^{2} = 2 x + 8$

${x}^{2} - 2 x - 8 = 0$

Sum $= 2$, Product = $- 8$, therefore $x = 4 \mathmr{and} x = - 2$

The extraneous ones would be $x = 0 \mathmr{and} x = - 4$, because there would be zero denominator.