Whakaoti i te x+y+z=xyz

$$x + y + z = x y z$$

Whakaoti mō x

$$x=-\frac{y+z}{1-yz}$$

$$z=0\text{ or }y\neq \frac{1}{z}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te xyz mai i ngā taha e rua.

$$x+y+z-xyz=0$$

Tangohia te y mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x+z-xyz=-y$$

Tangohia te z mai i ngā taha e rua.

$$x-xyz=-y-z$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(1-yz\right)x=-y-z$$

Whakawehea ngā taha e rua ki te 1-yz.

$$\frac{\left(1-yz\right)x}{1-yz}=\frac{-y-z}{1-yz}$$

Mā te whakawehe ki te 1-yz ka wetekia te whakareanga ki te 1-yz.

$$x=\frac{-y-z}{1-yz}$$

Whakawehe -y-z ki te 1-yz.

$$x=-\frac{y+z}{1-yz}$$

Whakaoti mō y

$$y=-\frac{x+z}{1-xz}$$

$$z=0\text{ or }x\neq \frac{1}{z}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te xyz mai i ngā taha e rua.

$$x+y+z-xyz=0$$

Tangohia te x mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$y+z-xyz=-x$$

Tangohia te z mai i ngā taha e rua.

$$y-xyz=-x-z$$

Pahekotia ngā kīanga tau katoa e whai ana i te y.

$$\left(1-xz\right)y=-x-z$$

Whakawehea ngā taha e rua ki te 1-xz.

$$\frac{\left(1-xz\right)y}{1-xz}=\frac{-x-z}{1-xz}$$

Mā te whakawehe ki te 1-xz ka wetekia te whakareanga ki te 1-xz.

$$y=\frac{-x-z}{1-xz}$$

Whakawehe -x-z ki te 1-xz.

$$y=-\frac{x+z}{1-xz}$$