1) (x+6)(x-5)/(x^2-25) + 10/(x^2-25) = 4/3
3(x^2+x-30+10) = 4(x^2-25)
3x^2+3x-60 = 4x^2-100
x^2 - 3x - 40 = 0
(x-8)(x+5) = 0
x1 = - 5; x2 = 8
2) (x+3)(x+7)/(x^2-49) - 10(x-7)/(x^2-49) = 140/(x^2-49)
x^2+ 10x+21-10x+70 = 140
x^2+91 = 140
x^2 = 49
x1 = - 7; x2 = 7
3) (x+3)(x-1)/(x^2-1) + (x+1)(x+1)/(x^2-1) = 4/(x^2-1)
x^2+2x+3+x^2+2x+1 = 4
2x^2 + 4x = 0
2x(x+2) = 0
x1 = 0; x2 = - 2
4) (x+6)(x-9)/(x-4)(x-9) + 50/(x-4)(x-9) = - (x+9)(x-4)/(x-4)(x-9)
(x+6)(x-9) + 50 = - (x-4)(x+9)
x^2-3x+54+50 = - (x^2+5x-36)
2x^2 + 2x + 68 = 0
x^2 + x + 34 = 0
Решений нет.