Whakaoti i te 1/x+1/y=1/z

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

Whakaoti mō x

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

$$y\neq 0\text{ and }z\neq 0\text{ and }y\neq z$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te xyz, arā, te tauraro pātahi he tino iti rawa te kitea o x,y,z.

$$yz+xz=xy$$

Tangohia te xy mai i ngā taha e rua.

$$yz+xz-xy=0$$

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

$$xz-xy=-yz$$

Whakaraupapatia anō ngā kīanga tau.

$$-xy+xz=-yz$$

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

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te -y+z.

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

Mā te whakawehe ki te -y+z ka wetekia te whakareanga ki te -y+z.

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

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{yz}{z-y}\text{, }x\neq 0$$

Whakaoti mō y

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

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te xyz, arā, te tauraro pātahi he tino iti rawa te kitea o x,y,z.

$$yz+xz=xy$$

Tangohia te xy mai i ngā taha e rua.

$$yz+xz-xy=0$$

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

$$yz-xy=-xz$$

Whakaraupapatia anō ngā kīanga tau.

$$-xy+yz=-xz$$

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

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te z-x.

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

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

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

Tē taea kia ōrite te tāupe y ki 0.

$$y=-\frac{xz}{z-x}\text{, }y\neq 0$$