Help with algebra?

1.
(a² + b² - c² + 2ab) / (a² + c² - b² + 2ac)
= [(a² + 2ab + b²) - c²] / [(a² + 2ac + c²) - b²]
= [(a + b)² - c²] / [(a + c)² - b²]
= [(a + b + c)(a + b - c)] / [(a + c + b)(a + c - b)]
= [(a + b + c)(a + b - c)] / [(a + b + c)(a - b + c)]
= (a + b - c) / (a - b + c)


2.
[(a² + b² - c²)² - (a² - b² + c²)²] / (4ab² - 4abc)
= [(a² + b² - c²) + (a² - b² + c²)] [(a² + b² - c²) - (a² - b² + c²)] / 4ab(b - c)
= (a² + b² - c² + a² - b² + c²)(a² + b² - c² - a² + b² - c²) / 4ab(b - c)
= 2a²(2b² - 2c²) / 4ab(b - c)
= 4a²(b² - c²) / 4ab(b - c)
= 4a²(b + c)(b - c) / 4ab(b - c)
= a(b - c) / b
(The given answer is incorrect.)


3.
(a² - 9) / (ab + 9a² + 27a + 27)
= (a + 3)(a - 3) / (ab + 9a² + 27a + 27)

The denominator cannot be factorized, please check.


4.
[(a + b)² - 4] / (2a + 2b + 4)
= [(a + b)² - 2²] / 2(a + b + 2)
= (a + b + 2)(a + b - 2) / 2(a + b + 2)
= (a + b - 2) / 2