Simplify the expression

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1747242284/aptidude_questions/hjgpbdabza3lql0ntv8p.png)

Question

Simplify the expression

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1747242284/aptidude_questions/hjgpbdabza3lql0ntv8p.png)

Accepted Answer

Step 1: Observe the numerator: 4x² + 9y² - 12xy.
Step 2: Try to factor the numerator. It resembles the expansion of (a - b)² = a² - 2ab + b².
Step 3: Rewrite the numerator as (2x)² + (3y)² - 2 * 2x * 3y = (2x - 3y)².
Step 4: So, numerator = (2x - 3y)².
Step 5: The denominator is (3y - 2x).
Step 6: Note that (2x - 3y) = -(3y - 2x).
Step 7: Therefore, (2x - 3y)² / (3y - 2x) = (2x - 3y)(2x - 3y) / (3y - 2x) = (2x - 3y) * [ (2x - 3y) / (3y - 2x) ] = (2x - 3y) * (-1) = -(2x - 3y) = 3y - 2x.

Hence, the simplified expression is 3y - 2x.

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