Simplify : `(3^(a+2)-3^(a+1))/(4xx3^(a)-3^(a))`

Answer

To simplify the expression \((3^{(a+2)} - 3^{(a+1)}) / (4 \cdot 3^{a} - 3^{a})\), we can follow these steps:

### Step 1: Factor out common terms in the numerator
In the numerator, we have \(3^{(a+2)} - 3^{(a+1)}\). We can factor out the common term \(3^{(a+1)}\):

\[ 3^{(a+2)} - 3^{(a+1)} = 3^{(a+1)}(3 - 1) = 3^{(a+1)} \cdot 2 \]

### Step 2: Simplify the numerator
Now, substituting back into the original expression, we have:

\[ \frac{3^{(a+1)} \cdot 2}{4 \cdot 3^{a} - 3^{a}} \]

### Step 3: Simplify the denominator
In the denominator, we can factor out \(3^{a}\):

\[ 4 \cdot 3^{a} - 3^{a} = (4 - 1) \cdot 3^{a} = 3 \cdot 3^{a} \]

### Step 4: Substitute the simplified denominator
Now we can rewrite the expression:

\[ \frac{3^{(a+1)} \cdot 2}{3 \cdot 3^{a}} \]

### Step 5: Simplify the fraction
Now we can simplify the fraction:

\[ = \frac{2 \cdot 3^{(a+1)}}{3 \cdot 3^{a}} = \frac{2}{3} \cdot \frac{3^{(a+1)}}{3^{a}} = \frac{2}{3} \cdot 3^{(a+1 - a)} = \frac{2}{3} \cdot 3^{1} = \frac{2 \cdot 3}{3} = 2 \]

### Final Answer
Thus, the simplified expression is:

\[ \boxed{2} \]