1.) \( \frac{8-2^{x+2}}{2^{x+1}-4} \)

To simplify the expression \( \frac{8-2^{x+2}}{2^{x+1}-4} \), let's first rewrite it in a more manageable form. Notice that \( 2^{x+2} = 4 \cdot 2^x \) and \( 2^{x+1} = 2 \cdot 2^x \). Replacing these in the expression gives: \[ \frac{8 - 4 \cdot 2^x}{2 \cdot 2^x - 4} \] Now, we can factor out the common terms in the numerator and denominator. In the numerator, we can factor out 4: \[ \frac{4(2 - 2^x)}{2(2^x - 2)} \] Let's simplify further by canceling out the common factor of 2 in the denominator: \[ \frac{4(2 - 2^x)}{2(2^x - 2)} = \frac{4(2 - 2^x)}{2 \cdot (-(2 - 2^x))} = -2 \] Thus, the simplified expression is \( -2 \).