A) \( \frac{10 x^{2}-23 x+51}{x^{4}-x^{3}-11 x^{2}-x-12} \)

Did you know that rational expressions like the one you've presented can often be simplified by factoring? In this case, check if the numerator or the denominator can be factored into simpler polynomial expressions. It might reveal common factors that allow you to reduce the fraction into a simpler form! To properly work with these types of expressions, pay close attention to the domain restrictions. The denominator (in this case, \( x^4 - x^3 - 11x^2 - x - 12 \)) cannot equal zero. By finding the roots of the denominator, you ensure you're aware of any values of \( x \) that would make the expression undefined, keeping your math journey smooth and mistake-free!