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.