Solve for \( x \) \( x+\frac{6}{x+10}=\frac{5 x}{x+10} \) \( x= \) One or more solutions: No solution

Solve the equation \( x+\frac{6}{x+10}=\frac{5x}{x+10} \). Solve the equation by following steps: - step0: Solve for \(x\): \(x+\frac{6}{x+10}=\frac{5x}{x+10}\) - step1: Find the domain: \(x+\frac{6}{x+10}=\frac{5x}{x+10},x\neq -10\) - step2: Multiply both sides of the equation by LCD: \(\left(x+\frac{6}{x+10}\right)\left(x+10\right)=\frac{5x}{x+10}\times \left(x+10\right)\) - step3: Simplify the equation: \(x^{2}+10x+6=5x\) - step4: Move the expression to the left side: \(x^{2}+10x+6-5x=0\) - step5: Subtract the terms: \(x^{2}+5x+6=0\) - step6: Factor the expression: \(\left(x+2\right)\left(x+3\right)=0\) - step7: Separate into possible cases: \(\begin{align}&x+2=0\\&x+3=0\end{align}\) - step8: Solve the equation: \(\begin{align}&x=-2\\&x=-3\end{align}\) - step9: Check if the solution is in the defined range: \(\begin{align}&x=-2\\&x=-3\end{align},x\neq -10\) - step10: Find the intersection: \(\begin{align}&x=-2\\&x=-3\end{align}\) - step11: Rewrite: \(x_{1}=-3,x_{2}=-2\) The solutions to the equation \(x+\frac{6}{x+10}=\frac{5x}{x+10}\) are \(x=-3\) and \(x=-2\).