What is the solution set for (x-2)/(x+4)=2-(4/x)?

Aug 26, 2015

I found:
${x}_{1} = - 8$
${x}_{2} = 2$

Explanation:

We can use as common denominator: $x \left(x + 4\right)$ to get:
$\frac{x \left(x - 2\right)}{x \left(x + 4\right)} = \frac{2 x \left(x + 4\right) - 4 \left(x + 4\right)}{x \left(x + 4\right)}$
We can cancel out both denominators and multiply:
${x}^{2} - 2 x = 2 {x}^{2} + 8 x - 4 x - 16$ rearranging:
${x}^{2} + 6 x - 16 = 0$
${x}_{1 , 2} = \frac{- 6 \pm \sqrt{36 + 64}}{2} =$
${x}_{1 , 2} = \frac{- 6 \pm 10}{2} =$
${x}_{1} = - 8$
${x}_{2} = 2$