`((0.8xx0.8-0.9xx0.9)//(0.8xx1-0.9xx1))`

Options

A. 1.4
B. 1.17
C. 2
D. 1.7

Answer

To solve the expression \(\frac{(0.8 \times 0.8 - 0.9 \times 0.9)}{(0.8 \times 1 - 0.9 \times 1)}\), we can follow these steps:

### Step 1: Rewrite the expression
The expression can be rewritten as:
\[ \frac{(0.8^2 - 0.9^2)}{(0.8 - 0.9)} \]

### Step 2: Identify the difference of squares
We recognize that the numerator \(0.8^2 - 0.9^2\) is a difference of squares. We can use the identity:
\[ a^2 - b^2 = (a - b)(a + b) \]
Here, \(a = 0.8\) and \(b = 0.9\).

### Step 3: Apply the difference of squares identity
Using the identity, we can rewrite the numerator:
\[ 0.8^2 - 0.9^2 = (0.8 - 0.9)(0.8 + 0.9) \]
So, the expression now looks like:
\[ \frac{(0.8 - 0.9)(0.8 + 0.9)}{(0.8 - 0.9)} \]

### Step 4: Simplify the expression
Notice that \(0.8 - 0.9\) appears in both the numerator and the denominator. We can cancel these terms (as long as we note that \(0.8 - 0.9 \neq 0\)):
\[ 0.8 + 0.9 \]

### Step 5: Calculate the final value
Now, we can calculate:
\[ 0.8 + 0.9 = 1.7 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{1.7} \]