Whakaoti i te xyz+x+y+z+xy+xz+yz=1989

$$xyz+x+y+z+xy+xz+yz=1989$$

Whakaoti mō x

$$x=-\frac{yz+y+z-1989}{yz+y+z+1}$$

$$z\neq -1\text{ and }y\neq -1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te y mai i ngā taha e rua.

$$xyz+x+z+xy+xz+yz=1989-y$$

Tangohia te z mai i ngā taha e rua.

$$xyz+x+xy+xz+yz=1989-y-z$$

Tangohia te yz mai i ngā taha e rua.

$$xyz+x+xy+xz=1989-y-z-yz$$

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

$$\left(yz+1+y+z\right)x=1989-y-z-yz$$

He hanga arowhānui tō te whārite.

$$\left(yz+y+z+1\right)x=1989-z-y-yz$$

Whakawehea ngā taha e rua ki te yz+1+y+z.

$$\frac{\left(yz+y+z+1\right)x}{yz+y+z+1}=\frac{1989-z-y-yz}{yz+y+z+1}$$

Mā te whakawehe ki te yz+1+y+z ka wetekia te whakareanga ki te yz+1+y+z.

$$x=\frac{1989-z-y-yz}{yz+y+z+1}$$

Whakaoti mō y

$$y=-\frac{xz+x+z-1989}{xz+x+z+1}$$

$$z\neq -1\text{ and }x\neq -1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x mai i ngā taha e rua.

$$xyz+y+z+xy+xz+yz=1989-x$$

Tangohia te z mai i ngā taha e rua.

$$xyz+y+xy+xz+yz=1989-x-z$$

Tangohia te xz mai i ngā taha e rua.

$$xyz+y+xy+yz=1989-x-z-xz$$

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

$$\left(xz+1+x+z\right)y=1989-x-z-xz$$

He hanga arowhānui tō te whārite.

$$\left(xz+x+z+1\right)y=1989-z-x-xz$$

Whakawehea ngā taha e rua ki te xz+1+x+z.

$$\frac{\left(xz+x+z+1\right)y}{xz+x+z+1}=\frac{1989-z-x-xz}{xz+x+z+1}$$

Mā te whakawehe ki te xz+1+x+z ka wetekia te whakareanga ki te xz+1+x+z.

$$y=\frac{1989-z-x-xz}{xz+x+z+1}$$