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

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

Whakaoti mō y

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

$$x\neq -1$$

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.

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

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

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

Whakawehea ngā taha e rua ki te -x-1.

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

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

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

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

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

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{y\left(y+8\right)}+y}{4}$$

$$x=\frac{-\sqrt{y\left(y+8\right)}+y}{4}$$

Whakaoti mō x

$$x=\frac{\sqrt{y\left(y+8\right)}+y}{4}$$

$$x=\frac{-\sqrt{y\left(y+8\right)}+y}{4}\text{, }y\leq -8\text{ or }y\geq 0$$