\( 1 \leftarrow \quad \) Solve the following proportion for the variable \( x \) \[ \begin{array}{l}\frac{4}{x-4}=\frac{8}{x} \\ x=\square \text { (Type an integer or a simplified fraction.) }\end{array} \]

Solve the equation \( \frac{4}{x-4}=\frac{8}{x} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{4}{x-4}=\frac{8}{x}\) - step1: Find the domain: \(\frac{4}{x-4}=\frac{8}{x},x \in \left(-\infty,0\right)\cup \left(0,4\right)\cup \left(4,+\infty\right)\) - step2: Cross multiply: \(4x=\left(x-4\right)\times 8\) - step3: Simplify the equation: \(4x=8\left(x-4\right)\) - step4: Rewrite the expression: \(4x=4\times 2\left(x-4\right)\) - step5: Evaluate: \(x=2\left(x-4\right)\) - step6: Expand the expression: \(x=2x-8\) - step7: Move the variable to the left side: \(x-2x=-8\) - step8: Subtract the terms: \(-x=-8\) - step9: Change the signs: \(x=8\) - step10: Check if the solution is in the defined range: \(x=8,x \in \left(-\infty,0\right)\cup \left(0,4\right)\cup \left(4,+\infty\right)\) - step11: Find the intersection: \(x=8\) The solution to the proportion is \( x = 8 \).