5. \( \frac{2}{x+4}-\frac{1}{x}=\frac{2}{3 x} \)

Solve the equation \( \frac{2}{x+4}-\frac{1}{x}=\frac{2}{3x} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{2}{x+4}-\frac{1}{x}=\frac{2}{3x}\) - step1: Find the domain: \(\frac{2}{x+4}-\frac{1}{x}=\frac{2}{3x},x \in \left(-\infty,-4\right)\cup \left(-4,0\right)\cup \left(0,+\infty\right)\) - step2: Multiply both sides of the equation by LCD: \(\left(\frac{2}{x+4}-\frac{1}{x}\right)\times 3x\left(x+4\right)=\frac{2}{3x}\times 3x\left(x+4\right)\) - step3: Simplify the equation: \(3x-12=2x+8\) - step4: Move the expression to the left side: \(3x-2x=8+12\) - step5: Add and subtract: \(x=8+12\) - step6: Add and subtract: \(x=20\) - step7: Check if the solution is in the defined range: \(x=20,x \in \left(-\infty,-4\right)\cup \left(-4,0\right)\cup \left(0,+\infty\right)\) - step8: Find the intersection: \(x=20\) The solution to the equation \( \frac{2}{x+4}-\frac{1}{x}=\frac{2}{3x} \) is \( x=20 \).