Если дробь равна 0, то числитель равен 0, а знаменатель нет.
1) x = -4
2) (x-3)(x+3)/(x-3) = x+3 = 0
x = -3
3) (x+5)/(x^2-25) = (x+5) / ((x+5)(x-5)) = 1/(x-5) = 0
Решений нет
4) (3(x+4) - 2(x-4)) / ((x+4)(x-4)) = (3x+12-2x+8)/(x^2-16) = (x+20)/(x^2-16) = 0
x = -20
5) (x+2-3)/(x+2) = (2x+1-2)/(2x+1)
1 - 3/(x+2) = 1 - 2/(2x+1)
3/(x+2) - 2/(2x+1) = 0
(3(2x+1) - 2(x+2)) / ((x+2)(2x+1)) = (6x+3-2x-4)/((x+2)(2x+1)) = 0
(4x-1)/((x+2)(2x+1)) = 0
x = 1/4
6) (3x-3-2)/(x-1) - (2x-4-1)/(x-2) = 1
3 - 2/(x-1) - 2 + 1/(x-2) = 1
1/(x-2) - 2/(x-1) = 0
(x-1 - 2(x-2)) / ((x-1)(x-2)) = (x-1-2x+4) / ((x-1)(x-2)) = (3-x) / ((x-1)(x-2)) = 0
x = 3
7) (x^2-1+10)/(x^2-1) = (x+1-3)/(x+1) + 5/(x-1)
1 + 10/(x^2-1) = 1 - 3/(x+1) + 5/(x-1)
10/(x^2-1) = (5(x+1) - 3(x-1)) / ((x+1)(x-1)) = (2x+8)/(x^2-1)
10 = 2x + 8
x = 1 - не подходит по области определения, поэтому решений нет
8) 1/(x^2-6x) + 1/(x^2+6x) = 2x/(x^2-36)
(x+6 + x-6)/(x(x+6)(x-6)) - 2x^2/(x(x^2-36)) = 0
(2x - 2x^2)/(x(x^2-36)) = 0
(2 - 2x)/(x^2-36) = 0
x = 1