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This looks like an exercise on simplifying algebraic expressions. Let's take a look at the questions provided:

1. (a) \(\frac{4x^2y + 2y^2}{2y^2}\)
2. (b) \(\frac{6x^2 - x - 1}{3x^2 - 5x - 2}\)
3. (c) \(\frac{6a^2 - 27a + 27}{8a^3 - 27}\)
4. (d) \(\frac{1 - x^2}{5x - x} \times 10x\)
5. (e) \(\frac{x^2 + x - 6}{2x - 8} \times \frac{x^2 - 16}{x^2 - 2x}\)
6. (f) \(\frac{2k^2 + k - 6}{k + 2} \div \left( (2k - 3) \right)\)

Would you like me to work through these problems and simplify each expression step by step? Let me know which one you would like to start with or if you'd like a full solution to all!

Simplify the following algebraic expressions:
1. (a) 4x^2y + 2y^2 / 2y^2
2. (b) 6x^2 - x - 1 / 3x^2 - 5x - 2
3. (c) 6a^2 - 27a + 27 / 8a^3 - 27
4. (d) (1 - x^2) / (5x - x) * 10x
5. (e) (x^2 + x - 6) / (2x - 8) * (x^2 - 16) / (x^2 - 2x)
6. (f) (2k^2 + k - 6) / (k + 2) ÷ (2k - 3)

Learn how to simplify various algebraic expressions including rational expressions and quadratic factorization. This problem set covers key algebra concepts like simplifying rational expressions, factoring quadratics, and using the difference of squares. Suitable for students in Grades 8-10.

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