Let’s evaluate the given expression step by step. The expression is:

$\left( \frac{a - b}{c + d} - (e \cdot f) \right) \cdot \left( \frac{g + h}{i} \cdot \left( (j - k) + l \right) \right)$

1. Analyze and Simplify Each Component:

Left-hand Side (LHS):

$\frac{a - b}{c + d} - (e \cdot f)$

• $\frac{a - b}{c + d}$: Perform the subtraction $a - b$, then divide by the sum $c + d$.
• $e \cdot f$: Multiply $e$ and $f$.
• Subtract the product $e \cdot f$ from $\frac{a - b}{c + d}$.

Right-hand Side (RHS):

$\frac{g + h}{i} \cdot \left( (j - k) + l \right)$

• $\frac{g + h}{i}$: Add $g + h$, then divide by $i$.
• $(j - k) + l$: Perform the subtraction $j - k$, then add $l$.
• Multiply the two results.

Final Expression:

After simplifying both sides, multiply the results from the LHS and RHS.

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2. General Strategy for Solution:

• Substitute numerical values if they are provided.
• Simplify inner parentheses first, then proceed to multiplication and division.

Would you like to solve it with specific values or leave it in symbolic form? Let me know! 😊

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Relative Questions:

1. Can I help with any specific values for $a, b, c, \dots, l$?
2. Would you like the expression evaluated symbolically using algebraic software?
3. Are you looking for simplification techniques for such expressions in general?
4. Would you like to break this down further for individual terms?
5. Is this part of a larger problem, such as calculus or physics?

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Tip:

When solving complex expressions, always simplify smaller components first (parentheses, fractions) before combining results for clarity and accuracy.