Whakaoti i te 2t-3t/t+3-t=t-1-2t/10-(t+3)

$$\frac { 2 t - 3 t } { t + 3 - t } = \frac { t - 1 - 2 t } { 10 - ( t + 3 ) }$$

Whakaoti mō t

$$t=1$$

$$t=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe t ki 7 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(t-7\right), arā, te tauraro pātahi he tino iti rawa te kitea o t+3-t,10-\left(t+3\right).

$$\left(t-7\right)\left(2t-3t\right)=-3\left(t-1-2t\right)$$

Pahekotia te 2t me -3t, ka -t.

$$\left(t-7\right)\left(-1\right)t=-3\left(t-1-2t\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te t-7 ki te -1.

$$\left(-t+7\right)t=-3\left(t-1-2t\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -t+7 ki te t.

$$-t^{2}+7t=-3\left(t-1-2t\right)$$

Pahekotia te t me -2t, ka -t.

$$-t^{2}+7t=-3\left(-t-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te -t-1.

$$-t^{2}+7t=3t+3$$

Tangohia te 3t mai i ngā taha e rua.

$$-t^{2}+7t-3t=3$$

Pahekotia te 7t me -3t, ka 4t.

$$-t^{2}+4t=3$$

Tangohia te 3 mai i ngā taha e rua.

$$-t^{2}+4t-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 4 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

Pūrua 4.

$$t=\frac{-4±\sqrt{16-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$t=\frac{-4±\sqrt{16+4\left(-3\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -3.

$$t=\frac{-4±\sqrt{16-12}}{2\left(-1\right)}$$

Tāpiri 16 ki te -12.

$$t=\frac{-4±\sqrt{4}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 4.

$$t=\frac{-4±2}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$t=\frac{-4±2}{-2}$$

Nā, me whakaoti te whārite t=\frac{-4±2}{-2} ina he tāpiri te ±. Tāpiri -4 ki te 2.

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

Whakawehe -2 ki te -2.

$$t=1$$

Nā, me whakaoti te whārite t=\frac{-4±2}{-2} ina he tango te ±. Tango 2 mai i -4.

$$t=-\frac{6}{-2}$$

Whakawehe -6 ki te -2.

$$t=3$$

Kua oti te whārite te whakatau.

$$t=1 t=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe t ki 7 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(t-7\right), arā, te tauraro pātahi he tino iti rawa te kitea o t+3-t,10-\left(t+3\right).

$$\left(t-7\right)\left(2t-3t\right)=-3\left(t-1-2t\right)$$

Pahekotia te 2t me -3t, ka -t.

$$\left(t-7\right)\left(-1\right)t=-3\left(t-1-2t\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te t-7 ki te -1.

$$\left(-t+7\right)t=-3\left(t-1-2t\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -t+7 ki te t.

$$-t^{2}+7t=-3\left(t-1-2t\right)$$

Pahekotia te t me -2t, ka -t.

$$-t^{2}+7t=-3\left(-t-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te -t-1.

$$-t^{2}+7t=3t+3$$

Tangohia te 3t mai i ngā taha e rua.

$$-t^{2}+7t-3t=3$$

Pahekotia te 7t me -3t, ka 4t.

$$-t^{2}+4t=3$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-t^{2}+4t}{-1}=\frac{3}{-1}$$

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

$$t^{2}+\frac{4}{-1}t=\frac{3}{-1}$$

Whakawehe 4 ki te -1.

$$t^{2}-4t=\frac{3}{-1}$$

Whakawehe 3 ki te -1.

$$t^{2}-4t=-3$$

Whakawehea te -4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2. Nā, tāpiria te pūrua o te -2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-4t+\left(-2\right)^{2}=-3+\left(-2\right)^{2}$$

Pūrua -2.

$$t^{2}-4t+4=-3+4$$

Tāpiri -3 ki te 4.

$$t^{2}-4t+4=1$$

Tauwehea t^{2}-4t+4. 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}.

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

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

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

Whakarūnātia.

$$t-2=1 t-2=-1$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$t=3 t=1$$