Whakaoti i te 1/x+1/y=1/4

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 4 }$$

Whakaoti mō x

$$x=-\frac{4y}{4-y}$$

$$y\neq 0\text{ and }y\neq 4$$

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 4xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y,4.

$$4y+4x=xy$$

Tangohia te xy mai i ngā taha e rua.

$$4y+4x-xy=0$$

Tangohia te 4y mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$4x-xy=-4y$$

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

$$\left(4-y\right)x=-4y$$

Whakawehea ngā taha e rua ki te 4-y.

$$\frac{\left(4-y\right)x}{4-y}=-\frac{4y}{4-y}$$

Mā te whakawehe ki te 4-y ka wetekia te whakareanga ki te 4-y.

$$x=-\frac{4y}{4-y}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{4y}{4-y}\text{, }x\neq 0$$

Whakaoti mō y

$$y=-\frac{4x}{4-x}$$

$$x\neq 0\text{ and }x\neq 4$$

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 4xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y,4.

$$4y+4x=xy$$

Tangohia te xy mai i ngā taha e rua.

$$4y+4x-xy=0$$

Tangohia te 4x mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$4y-xy=-4x$$

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

$$\left(4-x\right)y=-4x$$

Whakawehea ngā taha e rua ki te 4-x.

$$\frac{\left(4-x\right)y}{4-x}=-\frac{4x}{4-x}$$

Mā te whakawehe ki te 4-x ka wetekia te whakareanga ki te 4-x.

$$y=-\frac{4x}{4-x}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=-\frac{4x}{4-x}\text{, }y\neq 0$$