Whakaoti i te 1/x+1/y=1/15

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 15 }$$

Whakaoti mō x

$$x=-\frac{15y}{15-y}$$

$$y\neq 0\text{ and }y\neq 15$$

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 15xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y,15.

$$15y+15x=xy$$

Tangohia te xy mai i ngā taha e rua.

$$15y+15x-xy=0$$

Tangohia te 15y mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$15x-xy=-15y$$

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

$$\left(15-y\right)x=-15y$$

Whakawehea ngā taha e rua ki te 15-y.

$$\frac{\left(15-y\right)x}{15-y}=-\frac{15y}{15-y}$$

Mā te whakawehe ki te 15-y ka wetekia te whakareanga ki te 15-y.

$$x=-\frac{15y}{15-y}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{15y}{15-y}\text{, }x\neq 0$$

Whakaoti mō y

$$y=-\frac{15x}{15-x}$$

$$x\neq 0\text{ and }x\neq 15$$

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 15xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y,15.

$$15y+15x=xy$$

Tangohia te xy mai i ngā taha e rua.

$$15y+15x-xy=0$$

Tangohia te 15x mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$15y-xy=-15x$$

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

$$\left(15-x\right)y=-15x$$

Whakawehea ngā taha e rua ki te 15-x.

$$\frac{\left(15-x\right)y}{15-x}=-\frac{15x}{15-x}$$

Mā te whakawehe ki te 15-x ka wetekia te whakareanga ki te 15-x.

$$y=-\frac{15x}{15-x}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=-\frac{15x}{15-x}\text{, }y\neq 0$$