a) \( \frac{x^{2}-y^{2}}{3} \times \frac{6 x-3 y}{x^{3}+y^{3}} \) \( \begin{array}{ll}\text { a) } \frac{x^{2}+5 x+6}{2 x+4} \times \frac{x-3}{x^{2}-9} & \text { b) } \frac{2 x^{3}-16 y^{3}}{4 x+8 y} \times \frac{x^{2}-4 y^{2}}{x^{2}+2 x y+4 y^{2}} \\ \text { e) } \frac{x^{2}+4 x-45}{x^{2}-25} \div \frac{x^{2}-5 x+25}{x^{3}+125} & \text { d) } \frac{x^{2}+3 x-4}{x^{3}+64 y^{3}} \div \frac{x^{2}-1}{x^{2}-4 x y+16 y^{2}} \\ \text { g) } \frac{x^{2}-16}{x^{3}+64} \div \frac{3 x-12}{x^{2}-4 x+16} & \text { f) } \frac{a x+a y}{x^{2}-y^{2}} \times \frac{x^{2}+2 x y-3 y^{2}}{a} \\ \text { i) } \frac{8 x^{3}-27}{A x^{2}-9} \times \frac{8 x-12}{x^{2}+6 x+9} & \text { h) } \frac{x^{2}-6 x+5}{x^{2}+x+1} \div \frac{3 x-15}{x^{3}-1}\end{array} \)

Did you know that algebraic fractions have been used for centuries to solve complex problems? The concept of simplifying fractions dates back to ancient civilizations, like the Egyptians, who created early forms of mathematics to calculate areas and volumes using fractions. Simplifying and manipulating these fractions can make calculations easier and more manageable, definitely a skill to cherish! In the real world, fractions appear everywhere! From cooking recipes that require measuring ingredients, to financial calculations involving rates and percentages, understanding how to work with fractions helps in making informed decisions. Whether you’re scaling a recipe or distributing resources efficiently, mastering these little mathematical gems paves the way for clarity and precision!