The expression \(\frac{2x+5}{-4x+8}\) can be simplified by factoring the denominator, if possible.

### Steps to simplify:

1. Factor the denominator:
   \[
   -4x + 8 = -4(x - 2)
   \]
   So, the expression becomes:
   \[
   \frac{2x + 5}{-4(x - 2)}
   \]

2. Check if the numerator and denominator have any common factors. In this case, no common factors exist between \(2x + 5\) and \(-4(x - 2)\), so the expression cannot be simplified further.

### Final Simplified Form:
\[
\frac{2x + 5}{-4(x - 2)}
\]

Would you like more details on any step or further examples?

Here are 5 related questions:
1. How can I simplify other rational expressions?
2. How do you factor quadratic expressions?
3. What is the difference between factoring and simplifying?
4. How do you deal with complex rational expressions?
5. What are common mistakes in simplifying fractions?

**Tip:** Always factor both the numerator and denominator to check for any possible cancellations before simplifying!

Learn how to simplify the rational expression (2x+5)/(-4x+8) by factoring and checking for common factors. This problem covers key algebraic concepts, such as factoring and simplifying rational expressions, and is suitable for students in Grades 9-12.

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