Решите уравнение х/х-2 - 7/х+2 = 8/х^2-4

Question

Решите уравнение х/х-2 - 7/х+2 = 8/х^2-4

Answer 1

х/х-2 - 7/х+2 = 8/х^2-4
x(x+2)-7(x-2)/x^2-4 = 8/x^2-4
x^2+2x-7x+14-8/x^2-4 = x^2-5x+6/x^2-4 = x^2-2x-3x+6/x^2-4 = x(x-3)-2(x-3)/x^2-4 = (x-3)(x-2)/(x-2)(x+2)= x-3/x+2