(b) Simplify the toum \( \frac{x^{2}+x-6}{2 x-8} \times \frac{x^{2}-16}{x^{2}-2 x} \) \( \begin{array}{ll}\text { (1) } & \text { (2) } \frac{x^{2}+x}{x^{2}} \div \frac{x^{2}+2 x+1}{x^{3}} \\ \text { (3) } \frac{x^{2}-4 x y+4 y^{2}}{2 x-4} \div \frac{x-2 y}{x-2} \times \frac{x^{2}-4}{4} & \text { (4) } \frac{6+k-k^{2}}{3+3 k} \div(k-3) \div \frac{2 k+4}{k^{2}-1} \\ \text { (5) } \frac{2 k^{2}+k-6}{2 k^{2}-0} \times \frac{k^{4}-9}{x+2} \div(2 k-3) & \text { (6) } \frac{14-7 x}{x^{2}+x-2} \times \frac{x+2}{3 x-6}\end{array} \)

First additional information: The simplification of rational expressions often involves factoring polynomials, so understanding how to factor expressions like \(x^2 + x - 6\) (which factors into \((x + 3)(x - 2)\)) is essential. Meanwhile, dividing by polynomial expressions can often be flipped and multiplied, making the problem-solving much smoother. For instance, knowing to simplify \((x^2 - 16)\) into \((x - 4)(x + 4)\) can save you time and trouble! Second additional information: Real-world applications of rational expressions can be seen in a variety of real-life scenarios, such as in physics, where relations of distance, speed, and time often lead to creating and solving rational functions. Similarly, these rational expressions are pivotal when calculating rates or ratios in economics, such as profit margins or interest rates, emphasizing their practical significance beyond the classroom!