Whakaoti i te x^2y+2x^2-y-2=0

$$x ^ { 2 } y + 2 x ^ { 2 } - y - 2 = 0$$

Whakaoti mō y (complex solution)

$$\left\{\begin{matrix}\\y=-2\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=-1\text{ or }x=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x^{2}y-y-2=-2x^{2}$$

Me tāpiri te 2 ki ngā taha e rua.

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

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

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te x^{2}-1.

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

Mā te whakawehe ki te x^{2}-1 ka wetekia te whakareanga ki te x^{2}-1.

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

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

$$y=-2$$

Whakaoti mō y

$$\left\{\begin{matrix}\\y=-2\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&|x|=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x^{2}y-y-2=-2x^{2}$$

Me tāpiri te 2 ki ngā taha e rua.

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

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

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te x^{2}-1.

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

Mā te whakawehe ki te x^{2}-1 ka wetekia te whakareanga ki te x^{2}-1.

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

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

$$y=-2$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}\\x=1\text{; }x=-1\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=-2\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}\\x=1\text{; }x=-1\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=-2\end{matrix}\right.$$