It looks like you've uploaded a screenshot related to partial fractions decomposition. The problem involves determining constants $A$, $B$, $C$, and $D$ for the given expression.

To proceed with this, here's a breakdown of the steps you seem to be taking:

1. Starting Equation:
   The left-hand side expression is:
   $\frac{-5x^3 + 5x^2 + 16x + 36}{x^4 + 4x^3 + 9x^2}$ The right-hand side is set up with partial fractions:
   $\frac{A}{x} + \frac{B}{x^2} + \frac{C}{x^2 + 4x + 9} + \frac{D}{(x^2 + 4x + 9)}$ These are the unknown constants you're solving for.

2. Clearing Denominators:
   Multiply both sides of the equation by $x^4 + 4x^3 + 9x^2$ to eliminate the denominator.

3. Matching Coefficients:
   Expand the right-hand side and match the coefficients of corresponding powers of $x$ on both sides.

This kind of problem is typically solved by:

• Expanding the terms on the right-hand side.
• Grouping like powers of $x$.
• Equating coefficients of the corresponding powers of $x$ from the expanded form and the original polynomial on the left-hand side.

Would you like help expanding the terms or with solving for the constants $A$, $B$, $C$, and $D$? Let me know how I can assist further!

Here are a few related questions you might find useful:

1. How do we perform partial fraction decomposition for a repeated linear factor?
2. Can you explain how to expand the expression and group like terms?
3. What happens if we have higher powers of $x$ in the denominator?
4. How do we handle irreducible quadratic factors in partial fractions?
5. How can we solve for the constants once we have the expanded equation?

Tip: When expanding, always keep track of each term's degree to make sure you match the coefficients correctly.