https://r2.erweima.ai/mathbot/image/1725584080468y1chw6cs.jpg

I see that you've uploaded an image containing multiple mathematical expressions. I'll transcribe the equations and solve any of your choice. Let me know which specific problems you'd like help with.

Here are the transcribed equations:

1. \( \frac{x^2 + 10x + 21}{x + 3} \)
2. \( \frac{x^2 - 10x + 24}{x - 4} \)
3. \( \frac{x^2 - 4x - 45}{x + 5} \)
4. \( \frac{a^2 - b^2}{a - b} \)
5. \( \frac{2a^2 - ab - 3b^2}{a - b} \)
6. \( \frac{8m^2 - 2m}{2m} \)
7. \( \frac{100x(x-1)}{x - 1} \)
8. \( \frac{25 - b^2}{5 - b} \)
9. \( \frac{x^2 - 16}{x - 4} \)
10. \( \frac{4b^2 - 27}{b + 3} \)
11. \( \frac{x^2 - c^2}{x + c} \)
12. \( \frac{a^3 + 8}{a + 2} \)

Please let me know which problem(s) you'd like me to solve, and I'll provide the solution with detailed steps.

Solve the following algebraic fractions and expressions.

Learn how to solve algebraic fractions and rational expressions, including factored and quadratic expressions. This exercise covers key algebraic concepts, such as factoring, simplifying rational expressions, and solving quadratic equations. Suitable for students in Grades 8-10.

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