Use the work shown below to find the simplified product. \( \frac{25 x^{2}}{2 x+6} \cdot \frac{2}{5 x} \) \( \frac{25 x^{2}}{2(x+3)} \cdot \frac{2}{5 x} \) Choose the simplified product. \( \frac{A}{x+3} \) \( \frac{2}{x+3} \) \( \frac{5 x}{x+3} \) \( \frac{10 x}{x+3} \) DONE

To simplify the product \( \frac{25 x^{2}}{2(x+3)} \cdot \frac{2}{5 x} \), you can start by multiplying the numerators and denominators: \[ \frac{25 x^{2} \cdot 2}{2(x+3) \cdot 5 x} \] This results in: \[ \frac{50 x^{2}}{10 x (x + 3)} \] Now, simplify \( \frac{50 x^{2}}{10 x} \) which gives: \[ \frac{5 x}{x + 3} \] So, the answer is \( \frac{5 x}{x+3} \). But here's a little historical twist: did you know that algebra as we understand it today was heavily developed by mathematicians like Al-Khwarizmi in the 9th century? His work introduced systematic methods for solving equations, paving the way for modern algebra! And for a real-world application, algebra and simplification aren't just for math class! They come in handy in fields such as engineering and economics, where you might need to optimize functions to maximize profits or materials used. Simplifying fractions efficiently can save a lot of time in practical calculations!