12 What is the equation of the OA of $$ f(x)=\frac{(x+5)^{2}}{x-3} $$

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To find the **oblique asymptote** (also known as a **slant asymptote**) of the function:

$$
f(x) = \frac{(x + 5)^2}{x - 3}
$$

we can perform **polynomial long division**. The oblique asymptote is the linear part of the division when the degree of the numerator is exactly one more than the degree of the denominator.

### Step-by-Step Division:

1. **Expand the Numerator:**
   $$
   (x + 5)^2 = x^2 + 10x + 25
   $$
   
2. **Set Up the Division:**
   $$
   \frac{x^2 + 10x + 25}{x - 3}
   $$
   
3. **Divide $$x^2$$ by $$x$$:**
   $$
   x^2 \div x = x
   $$
   Multiply the divisor by $$x$$:
   $$
   x \times (x - 3) = x^2 - 3x
   $$
   Subtract this from the original numerator:
   $$
   (x^2 + 10x + 25) - (x^2 - 3x) = 13x + 25
   $$
   
4. **Divide $$13x$$ by $$x$$:**
   $$
   13x \div x = 13
   $$
   Multiply the divisor by $$13$$:
   $$
   13 \times (x - 3) = 13x - 39
   $$
   Subtract this from the current remainder:
   $$
   (13x + 25) - (13x - 39) = 64
   $$
   
5. **Final Result of Division:**
   $$
   \frac{x^2 + 10x + 25}{x - 3} = x + 13 + \frac{64}{x - 3}
   $$
   
   The **linear part** of this expression, $$x + 13$$, represents the **oblique asymptote**.

### Conclusion:

The **oblique asymptote** of the function $$ f(x) = \frac{(x + 5)^2}{x - 3} $$ is:

$$
\boxed{y = x + 13}
$$
The oblique asymptote of the function $$ f(x) = \frac{(x + 5)^2}{x - 3} $$ is $$ y = x + 13 $$.

12 What is the equation of the OA of \( f(x)=\frac{(x+5)^{2}}{x-3} \)

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