for the fractions in the equation \( \frac{3}{x}+\frac{2}{5}=\frac{1}{15} \)

To tackle this fraction equation like a math detective, first, find a common denominator. The least common multiple of the denominators \( x \), 5, and 15 is \( 15x \). Multiply every term by this common denominator to eliminate the fractions effortlessly: \[ 15x \left( \frac{3}{x}+\frac{2}{5}=\frac{1}{15} \right) \] This transforms the equation into \( 45 + 6x = x \) after simplification. Now, solve for \( x \) by bringing all terms involving \( x \) to one side! Once you bring your terms together, you'll see \( 5x = -45 \), giving you \( x = -9 \). Voila! You've solved for \( x \) while making it a fun mini-math adventure! Did you know that fractions date back to ancient Egypt? The Rhind Mathematical Papyrus, circa 1650 BC, contains some of the oldest known fraction calculations. They were expressed using unit fractions (like 1/2, 1/3) which were quite unique compared to today’s mixed fractions! Isn't it fascinating how math has evolved over time? If you're a fan of practical life applications, consider how fractions flourish in cooking recipes! Knowing how to scale a recipe—whether halving or doubling—requires you to manipulate fractions like a pro. Imagine adjusting a pizza recipe for a gathering; understanding fractions can elevate your culinary skills while saving you from a kitchen disaster! Now, that’s a slice of real-world fun!