[(3x + 5y)^2 – 60xy] \div [(3x – 5y)^2]

Given expression:

$[(3x + 5y)^2 - 60xy] \div [(3x - 5y)^2]$

Step 1: Expand $(3x + 5y)^2$

$ (3x + 5y)^2 = 9x^2 + 30xy + 25y^2 $

Numerator:

$ (9x^2 + 30xy + 25y^2) - 60xy = 9x^2 - 30xy + 25y^2 $

Step 2: Factorize the numerator

$ 9x^2 - 30xy + 25y^2 = (3x - 5y)^2 $

Step 3: Simplify the fraction

$ \frac{(3x - 5y)^2}{(3x - 5y)^2} = 1 $

✅ Answer: 1