Solve the equation. Enter any solution that checks as an integer or reduced fraction. Separate with commas if there is more than one solution. If there are no solutions, click the No Solution button. \( \frac{x}{x+2}+\frac{3}{x+7}=\frac{3 x-4}{x^{2}+9 x+14} \) One or more solutions:

Solve the equation \( \frac{x}{x+2}+\frac{3}{x+7}=\frac{3x-4}{x^{2}+9x+14} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{x}{x+2}+\frac{3}{x+7}=\frac{3x-4}{x^{2}+9x+14}\) - step1: Find the domain: \(\frac{x}{x+2}+\frac{3}{x+7}=\frac{3x-4}{x^{2}+9x+14},x \in \left(-\infty,-7\right)\cup \left(-7,-2\right)\cup \left(-2,+\infty\right)\) - step2: Multiply both sides of the equation by LCD: \(\left(\frac{x}{x+2}+\frac{3}{x+7}\right)\left(x+2\right)\left(x+7\right)=\frac{3x-4}{x^{2}+9x+14}\times \left(x+2\right)\left(x+7\right)\) - step3: Simplify the equation: \(x^{2}+10x+6=3x-4\) - step4: Move the expression to the left side: \(x^{2}+10x+6-\left(3x-4\right)=0\) - step5: Calculate: \(x^{2}+7x+10=0\) - step6: Factor the expression: \(\left(x+2\right)\left(x+5\right)=0\) - step7: Separate into possible cases: \(\begin{align}&x+2=0\\&x+5=0\end{align}\) - step8: Solve the equation: \(\begin{align}&x=-2\\&x=-5\end{align}\) - step9: Check if the solution is in the defined range: \(\begin{align}&x=-2\\&x=-5\end{align},x \in \left(-\infty,-7\right)\cup \left(-7,-2\right)\cup \left(-2,+\infty\right)\) - step10: Find the intersection: \(x=-5\) The solution to the equation \( \frac{x}{x+2}+\frac{3}{x+7}=\frac{3x-4}{x^{2}+9x+14} \) is \( x = -5 \).