Whakaoti i te 3d/frac{d{v_{1}}+d/v_{2}+d/v_{2}}=frac{3v_{1}v_{2}}{2v_{1}+v_{2}}

$$\frac { 3 d } { \frac { d } { v _ { 1 } } + \frac { d } { v _ { 2 } } + \frac { d } { v _ { 2 } } } = \frac { 3 v _ { 1 } v _ { 2 } } { 2 v _ { 1 } + v _ { 2 } }$$

Whakaoti mō d

$$d\neq 0$$

$$v_{1}\neq -\frac{v_{2}}{2}\text{ and }v_{1}\neq 0\text{ and }v_{2}\neq 0$$

Ngā Upane Otinga

Whakareatia ngā taha e rua o te whārite ki te 2v_{1}+v_{2}.

$$d^{-1}v_{1}v_{2}\times 3d=3v_{1}v_{2}$$

Whakaraupapatia anō ngā kīanga tau.

$$3\times \frac{1}{d}dv_{1}v_{2}=3v_{1}v_{2}$$

Me whakakore te 3 ki ngā taha e rua.

$$\frac{1}{d}dv_{1}v_{2}=v_{1}v_{2}$$

Tē taea kia ōrite te tāupe d ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te d.

$$1dv_{1}v_{2}=v_{1}v_{2}d$$

Tangohia te v_{1}v_{2}d mai i ngā taha e rua.

$$1dv_{1}v_{2}-v_{1}v_{2}d=0$$

Pahekotia te 1dv_{1}v_{2} me -v_{1}v_{2}d, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi d ahakoa.

$$d\in \mathrm{R}$$

Tē taea kia ōrite te tāupe d ki 0.

$$d\in \mathrm{R}\setminus 0$$

Whakaoti mō v_1 (complex solution)

$$v_{1}\in \mathrm{C}\setminus -\frac{v_{2}}{2},0$$

$$d\neq 0\text{ and }v_{2}\neq 0$$

Whakaoti mō v_1

$$v_{1}\in \mathrm{R}\setminus -\frac{v_{2}}{2},0$$

$$d\neq 0\text{ and }v_{2}\neq 0$$