Whakaoti i te 1/8=1/u+1/v

$$\frac { 1 } { 8 } = \frac { 1 } { u } + \frac { 1 } { v }$$

Whakaoti mō u

$$u=-\frac{8v}{8-v}$$

$$v\neq 0\text{ and }v\neq 8$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe u ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 8uv, arā, te tauraro pātahi he tino iti rawa te kitea o 8,u,v.

$$uv=8v+8u$$

Tangohia te 8u mai i ngā taha e rua.

$$uv-8u=8v$$

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

$$\left(v-8\right)u=8v$$

Whakawehea ngā taha e rua ki te v-8.

$$\frac{\left(v-8\right)u}{v-8}=\frac{8v}{v-8}$$

Mā te whakawehe ki te v-8 ka wetekia te whakareanga ki te v-8.

$$u=\frac{8v}{v-8}$$

Tē taea kia ōrite te tāupe u ki 0.

$$u=\frac{8v}{v-8}\text{, }u\neq 0$$

Whakaoti mō v

$$v=-\frac{8u}{8-u}$$

$$u\neq 0\text{ and }u\neq 8$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe v ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 8uv, arā, te tauraro pātahi he tino iti rawa te kitea o 8,u,v.

$$uv=8v+8u$$

Tangohia te 8v mai i ngā taha e rua.

$$uv-8v=8u$$

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

$$\left(u-8\right)v=8u$$

Whakawehea ngā taha e rua ki te u-8.

$$\frac{\left(u-8\right)v}{u-8}=\frac{8u}{u-8}$$

Mā te whakawehe ki te u-8 ka wetekia te whakareanga ki te u-8.

$$v=\frac{8u}{u-8}$$

Tē taea kia ōrite te tāupe v ki 0.

$$v=\frac{8u}{u-8}\text{, }v\neq 0$$