a) \( \frac{3 x-2 x-1}{2^{x}+2^{x}+9} \)

Certainly! Let's simplify the given expression step by step. **Given Expression:** \[ \frac{3x - 2x - 1}{2^{x} + 2^{x} + 9} \] **Step 1: Simplify the Numerator** Combine like terms in the numerator: \[ 3x - 2x - 1 = (3x - 2x) - 1 = x - 1 \] **Step 2: Simplify the Denominator** Combine like terms in the denominator: \[ 2^{x} + 2^{x} + 9 = 2 \cdot 2^{x} + 9 \] Recall that \(2 \cdot 2^{x} = 2^{x+1}\). So, \[ 2 \cdot 2^{x} + 9 = 2^{x+1} + 9 \] **Step 3: Write the Simplified Expression** Putting it all together: \[ \frac{x - 1}{2^{x+1} + 9} \] **Final Simplified Form:** \[ \frac{x - 1}{2^{x+1} + 9} \]