Ответ:

x = 1/4

y = 1/3

z = 1/2

Пошаговое объяснение:

xy/(x + y) = 1/7

(x + y)/xy = 7

1/y + 1/x = 7

yz/(y + z) = 1/5

(y + z)/yz = 5

1/y + 1/z = 5

xz/(x + z) = 1/6

1/z + 1/x = 6

a = 1/x

b = 1/y

c = 1/z

a + b = 7  => a = 7 - b

b + c = 5  => c = 5 - b

c + a = 6

5 - b + 7 - b = 6

-2b = 6 - 12 = -6

b = 3

a = 7 - b = 4

c = 5 - b = 2

x = 1/4

y = 1/3

z = 1/2