To solve the expression step by step, we need to first write it out clearly and then simplify it accordingly.

The expression from the image is:

$\frac{11a}{6b^2y} - \frac{5x}{12y^4} - \frac{3p}{4} = \frac{Ay - Bx^2 + (C/D)y}{8(Dz)^2}$

Our task is to simplify the left-hand side so that it matches the right-hand side, and then fill in the values for $A$, $B$, $C$, and $D$.

Step 1: Simplify the left-hand side

The first step is to combine the terms on the left-hand side. However, we see that the left-hand side has no common denominators directly, and each fraction has distinct variables. Therefore, simplifying further isn't straightforward without more information, so it seems the problem might ask for direct comparison or extraction of components.

Step 2: Compare terms

We'll start by considering how the terms on the left side might correspond to the simplified right-hand side form.

Given: $\frac{Ay - Bx^2 + (C/D)y}{8(Dz)^2}$ This is one fraction with the denominator $8(Dz)^2$, implying that every term on the left side must also be expressed similarly, or it has been converted into this form.

Let's begin by finding a common denominator on the left side.

Expression: $\frac{11a}{6b^2y} - \frac{5x}{12y^4} - \frac{3p}{4}$

1. To make each term have the same denominator $8(Dz)^2$, we will compare coefficients directly to see how each term would match up.
2. Since the right-hand side implies terms of $y$, $x^2$, and possibly constant terms.

Conclusion:

Looking at the equation format and the lack of a complete like denominator on the left side, we assume $A$, $B$, $C$, and $D$ relate directly by direct term extraction, i.e., terms on the left being matched to those on the right.

• $A = 11a$
• $B = 5$
• $C = 3p$
• $D = 1$

So: $A = 11a, \quad B = 5, \quad C = 3p, \quad D = 1$

If this is correct:

1. $A = 11a$
2. $B = 5$
3. $C = 3p$
4. $D = 1$

Would you like further details on the process, or do you have any additional questions?

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Here are 8 related questions:

1. How do you simplify fractions with different denominators?
2. What techniques can be used to compare coefficients in an equation?
3. How can you find a common denominator for algebraic fractions?
4. What are the steps to equate coefficients in algebraic expressions?
5. How do you solve linear equations with multiple variables?
6. What is the importance of matching equation formats in algebra?
7. Can algebraic fractions always be simplified directly?
8. How do you handle subtraction of fractions with variables?

Tip: Always double-check the alignment of terms on both sides of the equation to ensure accurate matching.