(a) \( \frac{2^{x}+2^{x+2}}{2^{x+1}-2^{x}} \)

Let's simplify the expression \( \frac{2^{x}+2^{x+2}}{2^{x+1}-2^{x}} \) step by step. First, simplify the numerator: \[ 2^{x} + 2^{x+2} = 2^{x} + 2^{x} \cdot 2^2 = 2^{x} + 4 \cdot 2^{x} = 5 \cdot 2^{x} \] Now, simplify the denominator: \[ 2^{x+1} - 2^{x} = 2 \cdot 2^{x} - 2^{x} = (2 - 1) \cdot 2^{x} = 1 \cdot 2^{x} = 2^{x} \] Now we can rewrite the entire expression: \[ \frac{5 \cdot 2^{x}}{2^{x}} = 5 \] So, the simplified form of the expression \( \frac{2^{x}+2^{x+2}}{2^{x+1}-2^{x}} \) is \( 5 \).