Simiplify :
`(16xx2^(n+1)-4xx2^(n))/(16xx2^(n+2)-2xx2^(n+1))`

Explanation

To simplify the expression \((16 \times 2^{(n+1)} - 4 \times 2^{n}) / (16 \times 2^{(n+2)} - 2 \times 2^{(n+1)})\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the original expression:
\[ \frac{16 \times 2^{(n+1)} - 4 \times 2^{n}}{16 \times 2^{(n+2)} - 2 \times 2^{(n+1)}} \]

### Step 2: Factor out common terms
In the numerator, we can factor out \(2^{n}\):
\[ = \frac{2^{n}(16 \times 2 - 4)}{16 \times 2^{(n+2)} - 2 \times 2^{(n+1)}} \]
In the denominator, we can factor out \(2^{(n+1)}\):
\[ = \frac{2^{n}(16 \times 2 - 4)}{2^{(n+1)}(16 \times 2 - 2)} \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ = \frac{2^{n}(32 - 4)}{2^{(n+1)}(32 - 2)} \]
This simplifies to:
\[ = \frac{2^{n} \times 28}{2^{(n+1)} \times 30} \]

### Step 4: Cancel out the common terms
We can cancel \(2^{n}\) in the numerator and denominator:
\[ = \frac{28}{2 \times 30} \]
This simplifies further to:
\[ = \frac{28}{60} \]

### Step 5: Reduce the fraction
Now, we can reduce \(\frac{28}{60}\) by dividing both the numerator and denominator by 4:
\[ = \frac{7}{15} \]

### Final Answer
Thus, the simplified expression is:
\[ \frac{7}{15} \]