`(2.3xx2.3xx2.3-1)/(2.3xx2.3+2.3+1)=?`

Options

A. `0.3`
B. `1.3`
C. `2.2`
D. `3.3`

Answer

To solve the expression \((2.3 \times 2.3 \times 2.3 - 1) / (2.3 \times 2.3 + 2.3 + 1)\), we can use the algebraic identities for cubes and squares.

### Step-by-Step Solution:

1. **Identify the expression**:
We have the expression \((2.3^3 - 1) / (2.3^2 + 2.3 + 1)\).

2. **Recognize the identity**:
We can apply the difference of cubes identity, which states that \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\). Here, \(a = 2.3\) and \(b = 1\).

3. **Apply the difference of cubes**:
\[ 2.3^3 - 1^3 = (2.3 - 1)(2.3^2 + 2.3 \cdot 1 + 1^2) \]
This simplifies to:
\[ (2.3 - 1)(2.3^2 + 2.3 + 1) \]

4. **Calculate \(2.3 - 1\)**:
\[ 2.3 - 1 = 1.3 \]

5. **Substitute back into the expression**:
The numerator becomes:
\[ (1.3)(2.3^2 + 2.3 + 1) \]
The denominator remains:
\[ 2.3^2 + 2.3 + 1 \]

6. **Simplify the expression**:
Now we can simplify:
\[ \frac{(1.3)(2.3^2 + 2.3 + 1)}{(2.3^2 + 2.3 + 1)} = 1.3 \]

### Final Answer:
\[ \frac{(2.3 \times 2.3 \times 2.3 - 1)}{(2.3 \times 2.3 + 2.3 + 1)} = 1.3 \]