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The solution to the equation is \( x = -4 \).

Would you like more details on how this solution was derived or have any other questions?

Here are some related questions you may find helpful:

1. How do we solve rational equations step by step?
2. What happens if we substitute \( x = -4 \) into the original equation to verify the solution?
3. Are there any other methods to solve rational equations besides the one used?
4. How do we find restrictions on the variable \( x \) in rational equations?
5. What happens to the equation if we add more terms or change the denominators?

**Tip:** Always check for extraneous solutions in rational equations by ensuring the solution doesn't make any denominator zero.

Solve the equation \( \frac{4}{x} + \frac{3}{x+2} = \frac{2x+2}{x^2 + 2x} + \frac{7}{2x+4} \).

Learn how to solve a complex rational equation involving multiple fractions and variables: \( \frac{4}{x} + \frac{3}{x+2} = \frac{2x+2}{x^2 + 2x} + \frac{7}{2x+4} \). This problem focuses on algebraic techniques like finding a common denominator and checking for extraneous solutions. Suitable for students in Grades 10-12.

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