Whakaoti i te y=y+1/x

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

Whakaoti mō x

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

$$y\neq -1\text{ and }y\neq 0$$

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. Whakareatia ngā taha e rua o te whārite ki te x.

$$yx=y+1$$

Whakawehea ngā taha e rua ki te y.

$$\frac{yx}{y}=\frac{y+1}{y}$$

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

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

Whakawehe y+1 ki te y.

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

Tē taea kia ōrite te tāupe x ki 0.

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

Whakaoti mō y

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

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \frac{y+1}{x} mai i ngā taha e rua.

$$y-\frac{y+1}{x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia y ki te \frac{x}{x}.

$$\frac{yx}{x}-\frac{y+1}{x}=0$$

Tā te mea he rite te tauraro o \frac{yx}{x} me \frac{y+1}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{yx-\left(y+1\right)}{x}=0$$

Mahia ngā whakarea i roto o yx-\left(y+1\right).

$$\frac{yx-y-1}{x}=0$$

Whakareatia ngā taha e rua o te whārite ki te x.

$$yx-y-1=0$$

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$yx-y=1$$

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

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

Whakawehea ngā taha e rua ki te x-1.

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

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

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