b) \( \frac{3^{x+2}-3^{x}}{3^{x+1}+3^{x}} \) \( \frac{5^{n+1}+5^{n+2}}{5^{n}+5^{n+1}} \)

Did you know that exponential functions like the ones in your expressions grow at astonishing rates? In fact, if you plot \(3^x\) or \(5^n\), you’ll see they start to ramp up almost vertically after a certain point! This characteristic makes them incredibly useful in modeling real-world phenomena, such as population growth, radioactive decay, and even financial investments. When working with exponential expressions, a common mistake is forgetting to apply the rules of exponents correctly. For instance, remember that \( a^{m+n} = a^m \cdot a^n \). In your equations, simplifying terms correctly and factoring out common bases will often make complex-looking fractions pop into simpler forms. Always double-check your work to avoid minor errors!