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

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

Whakaoti mō y

$$y=-\frac{z^{2}}{1-xz^{2}}$$

$$z\neq 0\text{ and }x\neq \frac{1}{z^{2}}$$

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 yz^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o z^{2},y.

$$xyz^{2}=y+z^{2}$$

Tangohia te y mai i ngā taha e rua.

$$xyz^{2}-y=z^{2}$$

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

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

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

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

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

$$y=\frac{z^{2}}{xz^{2}-1}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=\frac{z^{2}}{xz^{2}-1}\text{, }y\neq 0$$

Whakaoti mō x

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

$$z\neq 0\text{ and }y\neq 0$$