Answer
$\{4\}$
Work Step by Step
Step 1. Since $x^2+6x+8=(x+4)(x+2)$, we can multiply this expression on both sides to remove the denominators.
Step 2. We have $2x=x(x+2)-2(x+4)$, $2x=x^2+2x-2x-8$ and $x^2-2x-8=0$, which gives $x=-2,4$
Step 3. The domain requirements for the variable are $x\ne-4,-2$. Thus the solution is only $x=4$, or in set form $\{4\}$.
