докажите тождество ((1/(a+b+c)^2) - ( (1/(a-b-c)^2)) * ((a^2 - ( b+c)^2)^2)/4a(b-c))

1. Задано выражение ( для тождества должна быть правая часть):

((1 / (a + b + c)²) - ( (1 / (a - b - c)²)) * ((a² - (b + c)²)²) / 4 * a *(b - c));

2. Упростим первый сомножитель:

1 / (a + b + c)²) - ( (1 / (a - b - c)² = (1 / (a + b + c))² - (1 / (a - b - c))² =

(1 / (a + b + c) + 1 / (a - b - c)) * (1 / (a + b + c) - 1 / (a - b - c)) =

(((a - b - c) + (a + b + c)) / (a + b + c) * (a - b - c)) *

(((a - b - c) - (a + b + c)) / (a + b + c) * (a - b - c)) =

((2 * a) * (-2) * (b + c)) / ((a + b + c)² * (a - b - c)²) =

((-4) * a * (b +c)) / ((a + b + c)² * (a - b - c)²);

3. Второй сомножитель:

((a² - (b + c)²)² = ((a + (b + c)) * (a - (b + c)))² =

(a + (b + c))² * (a - b - c)²;

4. Собираем вместе:

((-4) * a * (b +c)) / ((a + b + c)² * (a - b - c)²) *

((a + (b + c))² * (a - b - c)² / (4 * a * (b - c))) =

((-4) * a * (b +c)) / (4 * a * (b - c)) = -(b +c) / (b - c) = (b +c) / (c - b).