Whakaoti i te 1/x+2/y=1

$$\frac { 1 } { x } + \frac { 2 } { y } = 1$$

Whakaoti mō x

$$x=-\frac{y}{2-y}$$

$$y\neq 0\text{ and }y\neq 2$$

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 xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y.

$$y+x\times 2=xy$$

Tangohia te xy mai i ngā taha e rua.

$$y+x\times 2-xy=0$$

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

$$x\times 2-xy=-y$$

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

$$\left(2-y\right)x=-y$$

Whakawehea ngā taha e rua ki te 2-y.

$$\frac{\left(2-y\right)x}{2-y}=-\frac{y}{2-y}$$

Mā te whakawehe ki te 2-y ka wetekia te whakareanga ki te 2-y.

$$x=-\frac{y}{2-y}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{y}{2-y}\text{, }x\neq 0$$

Whakaoti mō y

$$y=-\frac{2x}{1-x}$$

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

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 xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y.

$$y+x\times 2=xy$$

Tangohia te xy mai i ngā taha e rua.

$$y+x\times 2-xy=0$$

Tangohia te x\times 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$y-xy=-x\times 2$$

Whakareatia te -1 ki te 2, ka -2.

$$y-xy=-2x$$

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

$$\left(1-x\right)y=-2x$$

Whakawehea ngā taha e rua ki te 1-x.

$$\frac{\left(1-x\right)y}{1-x}=-\frac{2x}{1-x}$$

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

$$y=-\frac{2x}{1-x}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=-\frac{2x}{1-x}\text{, }y\neq 0$$