Пускай 1/х = a
1/y = b
1/z = c
a + b = 1/2
b + c = 1/4 из него b = 1/4 - c
a + c = 1/8 из него a = 1/8 - c
Подставим a, b в первое уравнение a + b = 1/2
1/8 - c + 1/4 - c = 1/2
-2c = 1/2 - 1/4 - 1/8
- 2c = 4/8 - 2/8 - 1/8
-2c = 1/8
c = - 1/16
b = 1/4 - c b = 1/4 - (- 1/16) = 4/16 + 1/16 = 5/16
a = 1/8 - c a = 1/8 - (-1/16) = 2/16 + 1/16 = 3/16
a = 3/16 = 1 / (16/3) x = 16/3
b = 5/16 = 1 / (16/5) = 1/3,2 b = 3,2
c = -1/16 z = -16
Ответ проверил