Б) (3x - 1)/(x + 3) - (x - 2)/(x - 3) = 1
ОДЗ:
x ≠ -3; 3
Умножим всё уравнение на (x - 3)(x + 3):
(3x - 1)(x - 3) - (x - 2)(x + 3) = (x - 3)(x + 3)
3x² - 9x - x + 3 - (x² + 3x - 2x - 6) = x² - 9
3x² - 10x + 3 - x² - x + 6 - x² + 9 = 0
x² - 11x + 18 = 0
x² - 9x - 2x + 18 = 0
x(x - 9) - 2(x - 9) = 0
(x - 2)(x - 9) = 0
x = 2; 9.
Ответ: x = 2; 9.
x/(x² - 2x) - 6/(4 - x²) = 3/(x² + 2x)
x/x(x - 2) - 6/(2 - x)(x + 2) - 3/x(x + 2) = 0
ОДЗ:
x ≠ -2; 0; 2.
1/(x - 2) + 6/(x - 2)(x + 2) - 3/x(x + 2) = 0
Умножим всё уравнение на x(x - 2)(x + 2)
x(x + 2) + 6x - 3(x - 2) = 0
x² + 2x + 6x - 3x - 6 = 0
x² + 5x - 6 = 0
x² + 6x - x - 6 = 0
x(x + 6) - (x + 6) = 0
(x - 1)(x + 6) = 0
x = -6; 1.
Ответ: x = -6; 1.