Question

Решите уравнение, первый день учёбы—первые проблемы

Answer 1

3/x - 4/(1-x) = (5-x)/(x²-1)

3/x - 4/(1-x) - (5-x)/(x²-1) = 0

3/x + 4/(x-1) - (5-x)/(x²-1) = 0

(3(x-1)(x+1)+4x(x+1)-x(5-x))/(x(x-1)(x+1)) = 0

(3x²-3+4x²+4x-5x+x²)/(x(x-1)(x+1)) = 0

(8x²-x-3)/(x(x-1)(x+1)) = 0

ОДЗ: x≠0; x≠1; x≠-1

8x² - x - 3 = 0

D = (-1)² - 4 * 8 * (-3) = 1 + 96 = 97

x₁,₂ = (1±√96)/16

Ответ: x₁=(1-√96)/16; x₂= (1+√96)/16