The rational expression $$ \frac{x^{2}-8 x+15}{x^{2}-5 x+6} $$ simplifies to a.) $$ \frac{x-3}{x-2} $$ b.) $$ \frac{x-5}{x-3} $$ c.) $$ \frac{x-2}{x-5} $$ d.) $$ \frac{x-5}{x-2} $$

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To simplify the rational expression:

$$
\frac{x^{2} - 8x + 15}{x^{2} - 5x + 6}
$$

**Step 1: Factor the Numerator and the Denominator**

1. **Numerator:** $$ x^{2} - 8x + 15 $$
   $$
   x^{2} - 8x + 15 = (x - 3)(x - 5)
   $$

2. **Denominator:** $$ x^{2} - 5x + 6 $$
   $$
   x^{2} - 5x + 6 = (x - 2)(x - 3)
   $$

**Step 2: Simplify the Expression**

Substitute the factored forms back into the original expression:

$$
\frac{(x - 3)(x - 5)}{(x - 2)(x - 3)}
$$

Cancel the common factor $$(x - 3)$$ from the numerator and the denominator:

$$
\frac{x - 5}{x - 2}
$$

**Final Simplified Form:**

$$
\frac{x - 5}{x - 2}
$$

**Answer:**  
**d.) $$ \frac{x-5}{x-2} $$**
The simplified form of the expression is $$ \frac{x-5}{x-2} $$.

The rational expression simplifies to
a.)
b.)
c.)
d.)

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The rational expression simplifies to a.) b.) c.) d.)