Whakaoti i te y^-1=x^3+1/2

$${ y }^{ -1 } = \frac{ { x }^{ 3 } +1 }{ 2 }$$

Whakaoti mō y (complex solution)

$$y=\frac{2}{x^{3}+1}$$

$$x\neq -1\text{ and }x\neq \frac{-\sqrt{3}i+1}{2}\text{ and }x\neq \frac{1+\sqrt{3}i}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2y^{-1}=x^{3}+1$$

Whakaraupapatia anō ngā kīanga tau.

$$2\times \frac{1}{y}=x^{3}+1$$

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te y.

$$2\times 1=yx^{3}+y$$

Whakareatia te 2 ki te 1, ka 2.

$$2=yx^{3}+y$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$yx^{3}+y=2$$

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

$$\left(x^{3}+1\right)y=2$$

Whakawehea ngā taha e rua ki te x^{3}+1.

$$\frac{\left(x^{3}+1\right)y}{x^{3}+1}=\frac{2}{x^{3}+1}$$

Mā te whakawehe ki te x^{3}+1 ka wetekia te whakareanga ki te x^{3}+1.

$$y=\frac{2}{x^{3}+1}$$

Whakawehe 2 ki te x^{3}+1.

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

Tē taea kia ōrite te tāupe y ki 0.

$$y=\frac{2}{\left(x+1\right)\left(x^{2}-x+1\right)}\text{, }y\neq 0$$

Whakaoti mō y

$$y=\frac{2}{x^{3}+1}$$

$$x\neq -1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2y^{-1}=x^{3}+1$$

Whakaraupapatia anō ngā kīanga tau.

$$2\times \frac{1}{y}=x^{3}+1$$

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te y.

$$2\times 1=yx^{3}+y$$

Whakareatia te 2 ki te 1, ka 2.

$$2=yx^{3}+y$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$yx^{3}+y=2$$

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

$$\left(x^{3}+1\right)y=2$$

Whakawehea ngā taha e rua ki te x^{3}+1.

$$\frac{\left(x^{3}+1\right)y}{x^{3}+1}=\frac{2}{x^{3}+1}$$

Mā te whakawehe ki te x^{3}+1 ka wetekia te whakareanga ki te x^{3}+1.

$$y=\frac{2}{x^{3}+1}$$

Whakawehe 2 ki te x^{3}+1.

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

Tē taea kia ōrite te tāupe y ki 0.

$$y=\frac{2}{\left(x+1\right)\left(x^{2}-x+1\right)}\text{, }y\neq 0$$

Whakaoti mō x (complex solution)

$$x=e^{\frac{2\pi i}{3}}\sqrt[3]{-1+\frac{2}{y}}$$

$$x=\sqrt[3]{-1+\frac{2}{y}}$$

$$x=e^{\frac{4\pi i}{3}}\sqrt[3]{-1+\frac{2}{y}}\text{, }y\neq 0$$

Whakaoti mō x

$$x=\sqrt[3]{-1+\frac{2}{y}}$$

$$y\neq 0$$