Whakaoti i te x(x+2)/x-1=0

$$\frac { x ( x + 2 ) } { x - 1 } = 0$$

Whakaoti mō x

$$x=-2$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x-1.

$$x\left(x+2\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+2.

$$x^{2}+2x=0$$

Tauwehea te x.

$$x\left(x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x+2=0.

$$x=0 x=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x-1.

$$x\left(x+2\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+2.

$$x^{2}+2x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}}}{2}$$

Tuhia te pūtakerua o te 2^{2}.

$$x=\frac{-2±2}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±2}{2} ina he tāpiri te ±. Tāpiri -2 ki te 2.

$$x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-2±2}{2} ina he tango te ±. Tango 2 mai i -2.

$$x=-\frac{4}{2}$$

Whakawehe -4 ki te 2.

$$x=-2$$

Kua oti te whārite te whakatau.

$$x=0 x=-2$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x-1.

$$x\left(x+2\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+2.

$$x^{2}+2x=0$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+2x+1^{2}=1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=1$$

Tauwehea x^{2}+2x+1. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=1$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{1}$$

Whakarūnātia.

$$x+1=1 x+1=-1$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=0 x=-2$$