1)x^3-27/x^2+4x-21+(x-4)^2/x^2-49=0 2) 4/x+1+3x/x-2=-1

1) Разложим на множители и сократим дроби:

(x^3 - 27)/(x^2 + 4x - 21) + (x - 7)^2/(x^2 - 49) = 0;
(x - 3)(x^2 + 3x + 9)/(x + 7)(x - 3) + (x - 7)^2/(x + 7)(x - 7) = 0;
(x^2 + 3x + 9)/(x + 7) + (x - 7)/(x + 7) = 0;
(x^2 + 3x + 9 + x - 7)/(x + 7) = 0;
(x^2 + 4x + 2)/(x + 7) = 0;
x^2 + 4x + 2 = 0;
D/4 = 2^2 - 2 = 4 - 2 = 2;
x = -2 2.

2) Умножим на (x + 1)(x - 2):

4/(x + 1) + 3x/(x - 2) = -1;
4(x - 2) + 3x(x + 1) + (x + 1)(x - 2) = 0;
4x - 8 + 3x^2 + 3x + x^2 - x - 2 = 0;
4x^2 + 6x - 10 = 0;
D/4 = 3^2 + 4 * 10 = 49;
x = (-3 49)/4 = (-3 7)/4;
x1 = (-3 - 7)/4 = -10/4 = -2,5;
x2 = (-3 + 7)/4 = 4/4 = 1.