https://file.aiquickdraw.com/mathbot/file/17267587273123d3hrpn7.jpg

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.

Simplify: (3p - 3) / (p^2 - 27p - 46) - (10p + 9). Express your answer as a single fraction in simplest form.

This problem involves simplifying a rational expression by subtracting a polynomial. The steps include factoring polynomials, finding a common denominator, and combining like terms. Suitable for students in Grades 9-12, this problem highlights key algebraic skills needed for simplifying rational expressions.

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