It looks like the text from the image has some errors in extraction. Based on what I can interpret, the problem asks you to simplify the expression:

$\frac{3p - 3}{p^2 - 27p - 46} - (10p + 9)$

I'll solve this algebraically and simplify the expression to a single fraction.

Steps to solve:

1. First, factor the denominator $p^2 - 27p - 46$ if possible.
2. Rewrite the second term $(10p + 9)$ as a fraction with the same denominator.
3. Combine the fractions and simplify.

Let me start by factoring the denominator and proceed with the solution.It appears that the denominator $p^2 - 27p - 46$ cannot be factored further using simple methods, so we will keep it as is.

Now, let's rewrite the second term $(10p + 9)$ as a fraction with the same denominator $p^2 - 27p - 46$, and then combine both terms into a single fraction.After combining the fractions, the simplified numerator is:

$-10p^3 + 261p^2 + 706p + 411$

Thus, the entire expression is:

$\frac{-10p^3 + 261p^2 + 706p + 411}{p^2 - 27p - 46}$

This is the simplified form of the given expression.

Would you like further clarification on any steps?

Here are five related questions:

1. How do you factor a quadratic equation like $p^2 - 27p - 46$?
2. What are the conditions to simplify fractions with polynomials?
3. How can we identify when an expression can be factored further?
4. Why is it important to have a common denominator when combining fractions?
5. What methods can be used to simplify cubic polynomials like $-10p^3 + 261p^2$?

Tip: Always check if the numerator and denominator share common factors to further simplify a rational expression.