Question

Помогите пожалуйста!!!
Нужно решить выражение:
$\frac{1}{1+x+xy} + \frac{1}{1+y+yz} +\frac{1}{1+z+zx}$
Дано:
xyz = 1

Answer 1

xyz = 1

z = 1/xy

1/(1 + x + xy) = 1/(1 + x + xy)

1/(1 + y + yz) = 1/(1 + y + y/xy) = 1 / (1 + y + 1/x) = 1/(x/x + yx/x + 1/x) = x/(x + xy + 1)

1/(1 + z + zx) = 1/(1 + 1/xy + x/xy) = 1/(xy/xy + 1/xy + x/xy) = xy/(1 + x + xy)

1/(1 + x + xy) + 1/(1 + y + yz) + 1/(1 + z + zx) = 1/(1 + x + xy) +x/(x + xy + 1)  + xy/(1 + x + xy) = (1 + x + xy) / (1 + x + xy) = 1