Solve the following equation :
`(3^(2)-8^(2))/((3+8)^(2))=`

Options

A. `(5)/(11)`
B. `(-3)/(11)`
C. `(3)/(11)`
D. `(-5)/(11)`

Answer

To solve the equation \((3^2 - 8^2) / ((3 + 8)^2)\), we can follow these steps:

### Step 1: Identify the components of the equation
We have:
- \(3^2\) which equals \(9\)
- \(8^2\) which equals \(64\)
- \(3 + 8\) which equals \(11\)

### Step 2: Substitute the values into the equation
Now substituting these values into the equation gives us:
\[ \frac{9 - 64}{(11)^2} \]

### Step 3: Simplify the numerator
Calculating the numerator:
\[ 9 - 64 = -55 \]
So, the equation now looks like:
\[ \frac{-55}{(11)^2} \]

### Step 4: Calculate \((11)^2\)
Calculating \((11)^2\):
\[ (11)^2 = 121 \]
Now we can rewrite the equation as:
\[ \frac{-55}{121} \]

### Step 5: Simplify the fraction
The fraction \(\frac{-55}{121}\) cannot be simplified further, so we leave it as is.

### Final Answer
Thus, the final answer is:
\[ \frac{-55}{121} \]