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

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

Whakaoti mō x

$$x=4$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$\left(x-2\right)\left(x-1\right)-\left(x-1\right)\left(x+2\right)=4-x^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x-1 ka whakakotahi i ngā kupu rite.

$$x^{2}-3x+2-\left(x-1\right)\left(x+2\right)=4-x^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x+2 ka whakakotahi i ngā kupu rite.

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

Hei kimi i te tauaro o x^{2}+x-2, kimihia te tauaro o ia taurangi.

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

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

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

Pahekotia te -3x me -x, ka -4x.

$$-4x+2+2=4-x^{2}$$

Tāpirihia te 2 ki te 2, ka 4.

$$-4x+4=4-x^{2}$$

Tangohia te 4 mai i ngā taha e rua.

$$-4x+4-4=-x^{2}$$

Tangohia te 4 i te 4, ka 0.

$$-4x=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$-4x+x^{2}=0$$

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.

$$x^{2}-4x=0$$

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

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

Tuhia te pūtakerua o te \left(-4\right)^{2}.

$$x=\frac{-\left(-4\right)±4}{2}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±4}{2}$$

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

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

Whakawehe 8 ki te 2.

$$x=4$$

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

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

Whakawehe 0 ki te 2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=4 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$\left(x-2\right)\left(x-1\right)-\left(x-1\right)\left(x+2\right)=4-x^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x-1 ka whakakotahi i ngā kupu rite.

$$x^{2}-3x+2-\left(x-1\right)\left(x+2\right)=4-x^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x+2 ka whakakotahi i ngā kupu rite.

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

Hei kimi i te tauaro o x^{2}+x-2, kimihia te tauaro o ia taurangi.

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

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

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

Pahekotia te -3x me -x, ka -4x.

$$-4x+2+2=4-x^{2}$$

Tāpirihia te 2 ki te 2, ka 4.

$$-4x+4=4-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$-4x+4+x^{2}=4$$

Tangohia te 4 mai i ngā taha e rua.

$$-4x+x^{2}=4-4$$

Tangohia te 4 i te 4, ka 0.

$$-4x+x^{2}=0$$

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.

$$x^{2}-4x=0$$

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.

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

Pūrua -2.

$$x^{2}-4x+4=4$$

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

$$\left(x-2\right)^{2}=4$$

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{4}$$

Whakarūnātia.

$$x-2=2 x-2=-2$$

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

$$x=4 x=0$$