Whakaoti i te 2x/x-1=2x^2/x^2-x

$$\frac { 2 x } { x - 1 } = \frac { 2 x ^ { 2 } } { x ^ { 2 } - x }$$

Whakaoti mō x (complex solution)

$$x\in \mathrm{C}\setminus 1,0$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-1,x^{2}-x.

$$x\times 2x=2x^{2}$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}\times 2=2x^{2}$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$x^{2}\times 2-2x^{2}=0$$

Pahekotia te x^{2}\times 2 me -2x^{2}, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

$$x\in \mathrm{C}$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 1,0.

$$x\in \mathrm{C}\setminus 0,1$$

Whakaoti mō x

$$x\in \mathrm{R}\setminus 1,0$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-1,x^{2}-x.

$$x\times 2x=2x^{2}$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}\times 2=2x^{2}$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$x^{2}\times 2-2x^{2}=0$$

Pahekotia te x^{2}\times 2 me -2x^{2}, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

$$x\in \mathrm{R}$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 1,0.

$$x\in \mathrm{R}\setminus 0,1$$