Whakaoti i te x/x-x-1/3=06

$$\frac { x } { x } - \frac { x - 1 } { 3 } = 06$$

Whakaoti mō x

$$x=4$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.

$$3x-x\left(x-1\right)=0\times 6\times 3x$$

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

$$3x-\left(x^{2}-x\right)=0\times 6\times 3x$$

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

$$3x-x^{2}-\left(-x\right)=0\times 6\times 3x$$

Ko te tauaro o -x ko x.

$$3x-x^{2}+x=0\times 6\times 3x$$

Pahekotia te 3x me x, ka 4x.

$$4x-x^{2}=0\times 6\times 3x$$

Whakareatia te 0 ki te 6, ka 0.

$$4x-x^{2}=0\times 3x$$

Whakareatia te 0 ki te 3, ka 0.

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

Ko te tau i whakarea ki te kore ka hua ko te kore.

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

Tauwehea te x.

$$x\left(4-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 4-x=0.

$$x=0 x=4$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.

$$3x-x\left(x-1\right)=0\times 6\times 3x$$

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

$$3x-\left(x^{2}-x\right)=0\times 6\times 3x$$

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

$$3x-x^{2}-\left(-x\right)=0\times 6\times 3x$$

Ko te tauaro o -x ko x.

$$3x-x^{2}+x=0\times 6\times 3x$$

Pahekotia te 3x me x, ka 4x.

$$4x-x^{2}=0\times 6\times 3x$$

Whakareatia te 0 ki te 6, ka 0.

$$4x-x^{2}=0\times 3x$$

Whakareatia te 0 ki te 3, ka 0.

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

Ko te tau i whakarea ki te kore ka hua ko te kore.

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

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}.

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

Tuhia te pūtakerua o te 4^{2}.

$$x=\frac{-4±4}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-4±4}{-2}$$

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

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

Whakawehe 0 ki te -2.

$$x=0$$

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

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

Whakawehe -8 ki te -2.

$$x=4$$

Kua oti te whārite te whakatau.

$$x=0 x=4$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.

$$3x-x\left(x-1\right)=0\times 6\times 3x$$

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

$$3x-\left(x^{2}-x\right)=0\times 6\times 3x$$

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

$$3x-x^{2}-\left(-x\right)=0\times 6\times 3x$$

Ko te tauaro o -x ko x.

$$3x-x^{2}+x=0\times 6\times 3x$$

Pahekotia te 3x me x, ka 4x.

$$4x-x^{2}=0\times 6\times 3x$$

Whakareatia te 0 ki te 6, ka 0.

$$4x-x^{2}=0\times 3x$$

Whakareatia te 0 ki te 3, ka 0.

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

Ko te tau i whakarea ki te kore ka hua ko te kore.

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

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 ngā taha e rua ki te -1.

$$\frac{-x^{2}+4x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\frac{4}{-1}x=\frac{0}{-1}$$

Whakawehe 4 ki te -1.

$$x^{2}-4x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

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

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 te x^{2}-4x+4. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe 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.

$$x=4 x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=4$$