Simplify : `(999813xx999815+1)/((999814)^(2))`

Answer

To simplify the expression \((999813 \times 999815 + 1) / (999814)^2\), we can follow these steps:

### Step 1: Rewrite the Expression
We start with the expression:
\[ \frac{999813 \times 999815 + 1}{(999814)^2} \]

### Step 2: Recognize the Form of the Numerator
Notice that \(999813\) can be written as \(999814 - 1\) and \(999815\) can be written as \(999814 + 1\). Thus, we can rewrite the numerator:
\[ 999813 \times 999815 = (999814 - 1)(999814 + 1) \]

### Step 3: Apply the Difference of Squares Identity
Using the difference of squares identity, \(a^2 - b^2 = (a - b)(a + b)\), where \(a = 999814\) and \(b = 1\):
\[ (999814 - 1)(999814 + 1) = (999814)^2 - (1)^2 = (999814)^2 - 1 \]

### Step 4: Substitute Back into the Expression
Now substitute this back into the expression:
\[ 999813 \times 999815 + 1 = (999814)^2 - 1 + 1 = (999814)^2 \]

### Step 5: Simplify the Entire Expression
Now our expression becomes:
\[ \frac{(999814)^2}{(999814)^2} \]

### Step 6: Final Simplification
Since the numerator and denominator are the same, we can simplify this to:
\[ 1 \]

Thus, the simplified expression is:
\[ \boxed{1} \]