Whakaoti i te p+2=p+2/p-3

$$p + 2 = \frac { p + 2 } { p - 3 }$$

Whakaoti mō p

$$p=-2$$

$$p=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe p ki 3 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te p-3.

$$\left(p-3\right)p+\left(p-3\right)\times 2=p+2$$

Whakamahia te āhuatanga tohatoha hei whakarea te p-3 ki te p.

$$p^{2}-3p+\left(p-3\right)\times 2=p+2$$

Whakamahia te āhuatanga tohatoha hei whakarea te p-3 ki te 2.

$$p^{2}-3p+2p-6=p+2$$

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

$$p^{2}-p-6=p+2$$

Tangohia te p mai i ngā taha e rua.

$$p^{2}-p-6-p=2$$

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

$$p^{2}-2p-6=2$$

Tangohia te 2 mai i ngā taha e rua.

$$p^{2}-2p-6-2=0$$

Tangohia te 2 i te -6, ka -8.

$$p^{2}-2p-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-8\right)}}{2}$$

Pūrua -2.

$$p=\frac{-\left(-2\right)±\sqrt{4-4\left(-8\right)}}{2}$$

Whakareatia -4 ki te -8.

$$p=\frac{-\left(-2\right)±\sqrt{4+32}}{2}$$

Tāpiri 4 ki te 32.

$$p=\frac{-\left(-2\right)±\sqrt{36}}{2}$$

Tuhia te pūtakerua o te 36.

$$p=\frac{-\left(-2\right)±6}{2}$$

Ko te tauaro o -2 ko 2.

$$p=\frac{2±6}{2}$$

Nā, me whakaoti te whārite p=\frac{2±6}{2} ina he tāpiri te ±. Tāpiri 2 ki te 6.

$$p=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$p=4$$

Nā, me whakaoti te whārite p=\frac{2±6}{2} ina he tango te ±. Tango 6 mai i 2.

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

Whakawehe -4 ki te 2.

$$p=-2$$

Kua oti te whārite te whakatau.

$$p=4 p=-2$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe p ki 3 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te p-3.

$$\left(p-3\right)p+\left(p-3\right)\times 2=p+2$$

Whakamahia te āhuatanga tohatoha hei whakarea te p-3 ki te p.

$$p^{2}-3p+\left(p-3\right)\times 2=p+2$$

Whakamahia te āhuatanga tohatoha hei whakarea te p-3 ki te 2.

$$p^{2}-3p+2p-6=p+2$$

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

$$p^{2}-p-6=p+2$$

Tangohia te p mai i ngā taha e rua.

$$p^{2}-p-6-p=2$$

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

$$p^{2}-2p-6=2$$

Me tāpiri te 6 ki ngā taha e rua.

$$p^{2}-2p=2+6$$

Tāpirihia te 2 ki te 6, ka 8.

$$p^{2}-2p=8$$

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.

$$p^{2}-2p+1=8+1$$

Tāpiri 8 ki te 1.

$$p^{2}-2p+1=9$$

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

$$\left(p-1\right)^{2}=9$$

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

$$\sqrt{\left(p-1\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$p-1=3 p-1=-3$$

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

$$p=4 p=-2$$