Verified answer

(a - b)² = a² - 2ab + b²

a² - b² = (a - b)(a + b)

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b² - 18b - c² + 81 = (b - 9)² - c² = (b - 9 + c)(b - 9 - c)

b² + 2bc + c² - 9 - 9c = (b + c)² - 9(b + c) = (b + c)(b + c - 9)

(b - 9 + c)(b - 9 - c) / (b + c)(b + c - 9) = (b - 9 - c) / (b + c)