https://file.aiquickdraw.com/mathbot/file/1727201186193dzdirqbi.jpg

The expression in the image needs to be simplified. It can be written as:

\[
\frac{\frac{5}{x+5} - 7}{3 + \frac{4}{x+5}}
\]

### Steps to simplify:

1. **Combine terms in the numerator**:
   \[
   \frac{5}{x+5} - 7 = \frac{5 - 7(x+5)}{x+5} = \frac{5 - 7x - 35}{x+5} = \frac{-7x - 30}{x+5}
   \]

2. **Combine terms in the denominator**:
   \[
   3 + \frac{4}{x+5} = \frac{3(x+5) + 4}{x+5} = \frac{3x + 15 + 4}{x+5} = \frac{3x + 19}{x+5}
   \]

3. **Simplify the whole fraction**:
   \[
   \frac{\frac{-7x - 30}{x+5}}{\frac{3x + 19}{x+5}} = \frac{-7x - 30}{3x + 19}
   \]

So, the simplified form is:

\[
\frac{-7x - 30}{3x + 19}
\]

Would you like more details on any step or a further explanation?

Here are five relative questions to expand your understanding:

1. How do you simplify rational expressions with variables in both the numerator and denominator?
2. What happens when you have common denominators in complex fractions?
3. Can this simplified form be factored further?
4. How would the result change if additional constraints were placed on \( x \)?
5. Can you apply this approach to solve similar complex fraction problems?

**Tip:** Always look for common denominators when simplifying expressions, especially with complex fractions.

Simplify the complex rational expression: (5/(x+5) - 7) / (3 + 4/(x+5))

Learn how to simplify the complex rational expression (5/(x+5) - 7) / (3 + 4/(x+5)) through step-by-step breakdowns. This algebra problem covers combining fractions, simplifying complex fractions, and the use of the distributive property. Suitable for students in Grades 9-11.

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