Simplify $\dfrac{3 \cdot 2^n - 4 \cdot 2^{n-2}}{2^n - 2^{n-1}}$ (Example 2):

Factor $2^{n-2}$ from the numerator and $2^{n-1}$ from the denominator: numerator $=2^{n-2}(3\cdot 4-4)=2^{n-2}\cdot 8$, denominator $=2^{n-1}(2-1)=2^{n-1}$. The ratio is $2^{n-2}\cdot 8/2^{n-1}=8/2=4$.