Ta có: `(1)/(3x + yz)`

`= (1)/((x + y + z)x + yz)`

`= (1)/(x^2 + xy + xz + yz)`

`= (1)/(x(x + y) + z(x + y))`

`= (1)/((x + y)(x + z))`

Ta có: `(1)/(3y + xz)`

`= (1)/((x + y + z)y + xz)`

`= (1)/(xy + y^2 + yz + xz)`

`= (1)/(y(x + y) + z(y + x))`

`= (1)/((y + x)(y + z))`

Ta có: `(1)/(3z + xy)`

`= (1)/((x + y + z)z + xy)`

`= (1)/(xz + yz + z^2 + xy)`

`= (1)/(z(x + z) + y(z + x))`

`= (1)/((z + x)(z + y))`

Vậy:

`(1)/(3x + yz) + (1)/(3y + xz) + (1)/(3z + xy)`

`= (1)/((x + y)(x + z)) + (1)/((y + x)(y + z)) + (1)/((z + x)(z + y))`

`= (y + z + x + z + x + y)/((x + y)(y + z)(z + x))`

`= (2(x + y + z))/((x + y)(y + z)(z + x))`

`= (2.3)/((x + y)(y + z)(z + x))`

`= (6)/((x + y)(y + z)(z + x))` (đpcm)

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