Whakaoti i te w/z-xy/1-x-y=0

$$\frac { w } { z } - \frac { x y } { 1 - x } - y = 0$$

Whakaoti mō w

$$w=\frac{yz}{1-x}$$

$$z\neq 0\text{ and }x\neq 1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te z\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o z,1-x.

$$\left(x-1\right)w-\left(-zxy\right)-yz\left(x-1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-1 ki te w.

$$xw-w-\left(-zxy\right)-yz\left(x-1\right)=0$$

Ko te tauaro o -zxy ko zxy.

$$xw-w+zxy-yz\left(x-1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -yz ki te x-1.

$$xw-w+zxy-yzx+yz=0$$

Pahekotia te zxy me -yzx, ka 0.

$$xw-w+yz=0$$

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

$$xw-w=-yz$$

Whakaraupapatia anō ngā kīanga tau.

$$wx-w=-yz$$

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

$$\left(x-1\right)w=-yz$$

Whakawehea ngā taha e rua ki te x-1.

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

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

$$w=-\frac{yz}{x-1}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{w-yz}{w}\text{, }&y\neq 0\text{ and }z\neq 0\text{ and }w\neq 0\\x\neq 1\text{, }&w=0\text{ and }y=0\text{ and }z\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te z\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o z,1-x.

$$\left(x-1\right)w-\left(-zxy\right)-yz\left(x-1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-1 ki te w.

$$xw-w-\left(-zxy\right)-yz\left(x-1\right)=0$$

Ko te tauaro o -zxy ko zxy.

$$xw-w+zxy-yz\left(x-1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -yz ki te x-1.

$$xw-w+zxy-yzx+yz=0$$

Pahekotia te zxy me -yzx, ka 0.

$$xw-w+yz=0$$

Me tāpiri te w ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$xw+yz=w$$

Tangohia te yz mai i ngā taha e rua.

$$xw=w-yz$$

He hanga arowhānui tō te whārite.

$$wx=w-yz$$

Whakawehea ngā taha e rua ki te w.

$$\frac{wx}{w}=\frac{w-yz}{w}$$

Mā te whakawehe ki te w ka wetekia te whakareanga ki te w.

$$x=\frac{w-yz}{w}$$

Tē taea kia ōrite te tāupe x ki 1.

$$x=\frac{w-yz}{w}\text{, }x\neq 1$$