c) \( \frac{3 \cdot 2^{x}-2^{x-1}}{2^{x+2^{x+2}}} \)

To simplify the expression \( \frac{3 \cdot 2^{x}-2^{x-1}}{2^{x+2^{x+2}}} \), we can start by factoring out the common term in the numerator. Notice that \( 2^{x-1} = \frac{2^x}{2} \), so we can rewrite the numerator: \[ 3 \cdot 2^{x} - 2^{x-1} = 3 \cdot 2^{x} - \frac{2^{x}}{2} = 3 \cdot 2^{x} - \frac{1}{2} \cdot 2^{x} = \left( 3 - \frac{1}{2} \right) \cdot 2^{x} = \frac{6}{2} \cdot 2^{x} - \frac{1}{2} \cdot 2^{x} = \frac{5}{2} \cdot 2^{x}. \] Now substituting this back into the expression, we have: \[ \frac{\frac{5}{2} \cdot 2^{x}}{2^{x+2^{x+2}}}. \] Next, we can simplify the denominator: \[ 2^{x + 2^{x+2}} = 2^{x} \cdot 2^{2^{x+2}}. \] So the expression becomes: \[ \frac{\frac{5}{2} \cdot 2^{x}}{2^{x} \cdot 2^{2^{x+2}}} = \frac{5}{2} \cdot \frac{1}{2^{2^{x+2}}}. \] Finally, this simplifies to: \[ \frac{5}{2^{1 + 2^{x+2}}}. \] Thus, the simplified result of the expression is: \[ \frac{5}{2^{1 + 2^{x+2}}}. \]