Evaluate: `(1.2 xx 1.2 + 1.2 xx 0.3 + 0.3 xx 0.3)/(1.2 xx 1.2 xx 1.2- 0.3 xx 0.3 xx 0.3)`

Answer

To evaluate the expression \((1.2 \times 1.2 + 1.2 \times 0.3 + 0.3 \times 0.3)/(1.2 \times 1.2 \times 1.2 - 0.3 \times 0.3 \times 0.3)\), we can follow these steps:

### Step 1: Define Variables
Let \( A = 1.2 \) and \( B = 0.3 \). This allows us to rewrite the expression in terms of \( A \) and \( B \).

### Step 2: Rewrite the Expression
The expression can be rewritten as:
\[ \frac{A^2 + AB + B^2}{A^3 - B^3} \]

### Step 3: Use the Identity for \( A^3 - B^3 \)
Recall the identity:
\[ A^3 - B^3 = (A - B)(A^2 + AB + B^2) \]
Using this identity, we can substitute \( A^3 - B^3 \) in our expression:
\[ \frac{A^2 + AB + B^2}{(A - B)(A^2 + AB + B^2)} \]

### Step 4: Simplify the Expression
The \( A^2 + AB + B^2 \) in the numerator and denominator cancels out, leaving us with:
\[ \frac{1}{A - B} \]

### Step 5: Substitute Back the Values of \( A \) and \( B \)
Now we substitute back the values of \( A \) and \( B \):
\[ A - B = 1.2 - 0.3 = 0.9 \]
Thus, we have:
\[ \frac{1}{0.9} \]

### Step 6: Simplify the Fraction
To simplify \( \frac{1}{0.9} \):
\[ \frac{1}{0.9} = \frac{10}{9} \]

### Final Answer
Therefore, the value of the expression is:
\[ \frac{10}{9} \]

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