Solve for \( w \). \[ \frac{w}{w+4}=\frac{w+18}{w^{2}-16}-\frac{2}{w-4} \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Solve the equation \( \frac{w}{w+4}=\frac{w+18}{w^{2}-16}-\frac{2}{w-4} \). Solve the equation by following steps: - step0: Solve for \(w\): \(\frac{w}{w+4}=\frac{w+18}{w^{2}-16}-\frac{2}{w-4}\) - step1: Find the domain: \(\frac{w}{w+4}=\frac{w+18}{w^{2}-16}-\frac{2}{w-4},w \in \left(-\infty,-4\right)\cup \left(-4,4\right)\cup \left(4,+\infty\right)\) - step2: Multiply both sides of the equation by LCD: \(\frac{w}{w+4}\times \left(w+4\right)\left(w-4\right)=\left(\frac{w+18}{w^{2}-16}-\frac{2}{w-4}\right)\left(w+4\right)\left(w-4\right)\) - step3: Simplify the equation: \(w^{2}-4w=-w+10\) - step4: Move the expression to the left side: \(w^{2}-4w-\left(-w+10\right)=0\) - step5: Subtract the terms: \(w^{2}-3w-10=0\) - step6: Factor the expression: \(\left(w-5\right)\left(w+2\right)=0\) - step7: Separate into possible cases: \(\begin{align}&w-5=0\\&w+2=0\end{align}\) - step8: Solve the equation: \(\begin{align}&w=5\\&w=-2\end{align}\) - step9: Check if the solution is in the defined range: \(\begin{align}&w=5\\&w=-2\end{align},w \in \left(-\infty,-4\right)\cup \left(-4,4\right)\cup \left(4,+\infty\right)\) - step10: Find the intersection: \(\begin{align}&w=5\\&w=-2\end{align}\) - step11: Rewrite: \(w_{1}=-2,w_{2}=5\) The solutions to the equation are \( w = -2 \) and \( w = 5 \).