Whakaoti i te x^2=4x+1/y

$$x ^ { 2 } = \frac { 4 x + 1 } { y }$$

Whakaoti mō y

$$y=\frac{4x+1}{x^{2}}$$

$$x\neq -\frac{1}{4}\text{ and }x\neq 0$$

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

$$yx^{2}=4x+1$$

He hanga arowhānui tō te whārite.

$$x^{2}y=4x+1$$

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

$$\frac{x^{2}y}{x^{2}}=\frac{4x+1}{x^{2}}$$

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

$$y=\frac{4x+1}{x^{2}}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=\frac{4x+1}{x^{2}}\text{, }y\neq 0$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{y+4}+2}{y}$$

$$x=\frac{-\sqrt{y+4}+2}{y}\text{, }y\neq 0$$

Whakaoti mō x

$$x=\frac{\sqrt{y+4}+2}{y}$$

$$x=\frac{-\sqrt{y+4}+2}{y}\text{, }y\neq 0\text{ and }y\geq -4$$