`((0.96)^(3)-(0.1)^(3))/((0.96)^(2)+0.096+(0.1)^(2))` is simplified to :

Options

A. `1.06`
B. `0.95`
C. `0.86`
D. `0.97`

Answer

To simplify the expression \(\frac{(0.96)^3 - (0.1)^3}{(0.96)^2 + 0.096 + (0.1)^2}\), we can follow these steps:

### Step 1: Identify the values
Let \(a = 0.96\) and \(b = 0.1\).

### Step 2: Apply the difference of cubes formula
The numerator can be simplified using the difference of cubes formula, which states:
\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]
Thus, we can rewrite the numerator:
\[ (0.96)^3 - (0.1)^3 = (0.96 - 0.1)((0.96)^2 + (0.96)(0.1) + (0.1)^2) \]

### Step 3: Calculate \(a - b\)
Now, calculate \(a - b\):
\[ 0.96 - 0.1 = 0.86 \]

### Step 4: Calculate the second part of the numerator
Next, we need to calculate \((0.96)^2 + (0.96)(0.1) + (0.1)^2\):
- Calculate \((0.96)^2\):
\[ (0.96)^2 = 0.9216 \]
- Calculate \((0.96)(0.1)\):
\[ (0.96)(0.1) = 0.096 \]
- Calculate \((0.1)^2\):
\[ (0.1)^2 = 0.01 \]

Now, add these values together:
\[ 0.9216 + 0.096 + 0.01 = 1.0276 \]

### Step 5: Substitute back into the expression
Now substitute back into the expression:
\[ \frac{(0.96 - 0.1)((0.96)^2 + (0.96)(0.1) + (0.1)^2)}{(0.96)^2 + (0.96)(0.1) + (0.1)^2} \]
This simplifies to:
\[ \frac{0.86 \cdot 1.0276}{1.0276} \]

### Step 6: Cancel out the common terms
Since \((0.96)^2 + (0.96)(0.1) + (0.1)^2\) appears in both the numerator and denominator, we can cancel it out:
\[ 0.86 \]

### Final Answer
Thus, the simplified value of the expression is:
\[ \boxed{0.86} \]