Whakaoti i te 5x^3pi/6=4x/3y

$$\frac { 5 x ^ { 3 } \pi } { 6 } = \frac { 4 x } { 3 y }$$

Whakaoti mō y

$$\left\{\begin{matrix}y=\frac{8}{5\pi x^{2}}\text{, }&x\neq 0\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

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. Me whakarea ngā taha e rua o te whārite ki te 6y, arā, te tauraro pātahi he tino iti rawa te kitea o 6,3y.

$$y\times 5x^{3}\pi =2\times 4x$$

Whakareatia te 2 ki te 4, ka 8.

$$y\times 5x^{3}\pi =8x$$

He hanga arowhānui tō te whārite.

$$5\pi x^{3}y=8x$$

Whakawehea ngā taha e rua ki te 5x^{3}\pi .

$$\frac{5\pi x^{3}y}{5\pi x^{3}}=\frac{8x}{5\pi x^{3}}$$

Mā te whakawehe ki te 5x^{3}\pi ka wetekia te whakareanga ki te 5x^{3}\pi .

$$y=\frac{8x}{5\pi x^{3}}$$

Whakawehe 8x ki te 5x^{3}\pi .

$$y=\frac{8}{5\pi x^{2}}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=\frac{8}{5\pi x^{2}}\text{, }y\neq 0$$

Whakaoti mō x (complex solution)

$$x=\frac{2\sqrt{10}\left(\pi y\right)^{-\frac{1}{2}}}{5}$$

$$x=0$$

$$x=-\frac{2\sqrt{10}\left(\pi y\right)^{-\frac{1}{2}}}{5}\text{, }y\neq 0$$

Whakaoti mō x

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x=\frac{2\sqrt{\frac{10}{\pi y}}}{5}\text{; }x=-\frac{2\sqrt{\frac{10}{\pi y}}}{5}\text{, }&y>0\end{matrix}\right.$$