Simplify :
`(5^(n+4)-6xx5^(n+2))/(9xx5^(n+1)-5^(n+1)xx4)`

Explanation

To simplify the expression \((5^{n+4} - 6 \times 5^{n+2}) / (9 \times 5^{n+1} - 4 \times 5^{n+1})\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{5^{n+4} - 6 \times 5^{n+2}}{9 \times 5^{n+1} - 4 \times 5^{n+1}} \]

### Step 2: Factor out common terms in the numerator
In the numerator, we can factor out \(5^{n+2}\):
\[ 5^{n+4} = 5^{n+2} \times 5^2 = 5^{n+2} \times 25 \]
So, we can rewrite the numerator as:
\[ 5^{n+2}(25 - 6) \]
Thus, the numerator becomes:
\[ 5^{n+2}(19) \]

### Step 3: Factor out common terms in the denominator
In the denominator, we can factor out \(5^{n+1}\):
\[ 9 \times 5^{n+1} - 4 \times 5^{n+1} = (9 - 4) \times 5^{n+1} \]
So, the denominator becomes:
\[ 5^{n+1}(5) \]

### Step 4: Substitute back into the expression
Now we can substitute the factored forms back into the expression:
\[ \frac{5^{n+2} \times 19}{5^{n+1} \times 5} \]

### Step 5: Simplify the expression
Next, we can simplify the expression by canceling out \(5^{n+1}\) from the numerator and denominator:
\[ \frac{5^{n+2}}{5^{n+1}} = 5^{(n+2)-(n+1)} = 5^1 = 5 \]
Thus, we have:
\[ \frac{19 \times 5}{5} = 19 \]

### Final Answer
The simplified value of the expression is:
\[ \boxed{19} \]