$\frac{4 x}{x^{2}+2 x-8}-\frac{x}{x^{2}}=\frac{1}{x+4}$.

Step 1 ：Simplify the given equation by factoring the denominators of the fractions on the left side. The denominator of the first fraction can be factored into \((x-2)(x+4)\), and the denominator of the second fraction is already in its simplest form.

Step 2 ：Combine the fractions on the left side of the equation into a single fraction.

Step 3 ：Cross-multiply to get rid of the fractions and simplify the equation further. The simplified equation is \(\frac{1}{x + 4} = \frac{3x^2 - 2x + 8}{x(x^2 + 2x - 8)}\).

Step 4 ：Solve the equation. The solutions are complex numbers, which means that there are no real solutions to the equation.

Step 5 ：Final Answer: \(\boxed{\text{No real solutions}}\).