Whakaoti i te t/t^2-1=t/t+1

$$\frac { t } { t ^ { 2 } - 1 } = \frac { t } { t + 1 }$$

Whakaoti mō t

$$t=2$$

$$t=0$$

Ngā Upane Whakamahi Tauwehe

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

$$t=\left(t-1\right)t$$

Whakamahia te āhuatanga tohatoha hei whakarea te t-1 ki te t.

$$t=t^{2}-t$$

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

$$t-t^{2}=-t$$

Me tāpiri te t ki ngā taha e rua.

$$t-t^{2}+t=0$$

Pahekotia te t me t, ka 2t.

$$2t-t^{2}=0$$

Tauwehea te t.

$$t\left(2-t\right)=0$$

Hei kimi otinga whārite, me whakaoti te t=0 me te 2-t=0.

$$t=0 t=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$t=\left(t-1\right)t$$

Whakamahia te āhuatanga tohatoha hei whakarea te t-1 ki te t.

$$t=t^{2}-t$$

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

$$t-t^{2}=-t$$

Me tāpiri te t ki ngā taha e rua.

$$t-t^{2}+t=0$$

Pahekotia te t me t, ka 2t.

$$2t-t^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-t^{2}+2t=0$$

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}.

$$t=\frac{-2±\sqrt{2^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 2^{2}.

$$t=\frac{-2±2}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$t=\frac{-2±2}{-2}$$

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

$$t=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$t=0$$

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

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

Whakawehe -4 ki te -2.

$$t=2$$

Kua oti te whārite te whakatau.

$$t=0 t=2$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$t=\left(t-1\right)t$$

Whakamahia te āhuatanga tohatoha hei whakarea te t-1 ki te t.

$$t=t^{2}-t$$

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

$$t-t^{2}=-t$$

Me tāpiri te t ki ngā taha e rua.

$$t-t^{2}+t=0$$

Pahekotia te t me t, ka 2t.

$$2t-t^{2}=0$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-t^{2}+2t=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-t^{2}+2t}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$t^{2}+\frac{2}{-1}t=\frac{0}{-1}$$

Whakawehe 2 ki te -1.

$$t^{2}-2t=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$t^{2}-2t=0$$

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.

$$t^{2}-2t+1=1$$

Tauwehea t^{2}-2t+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}.

$$\left(t-1\right)^{2}=1$$

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

$$\sqrt{\left(t-1\right)^{2}}=\sqrt{1}$$

Whakarūnātia.

$$t-1=1 t-1=-1$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$t=2 t=0$$