Whakaoti i te 3/x^2-3x+1/x=2x/x^2-6x+9

$$\frac { 3 } { x ^ { 2 } - 3 x } + \frac { 1 } { x } = \frac { 2 x } { x ^ { 2 } - 6 x + 9 }$$

Whakaoti mō x

$$x=-3$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-3\right)^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-3x,x,x^{2}-6x+9.

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

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

$$3x-9+\left(x-3\right)^{2}=x\times 2x$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-3\right)^{2}.

$$3x-9+x^{2}-6x+9=x\times 2x$$

Pahekotia te 3x me -6x, ka -3x.

$$-3x-9+x^{2}+9=x\times 2x$$

Tāpirihia te -9 ki te 9, ka 0.

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

Whakareatia te x ki te x, ka x^{2}.

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

Tangohia te x^{2}\times 2 mai i ngā taha e rua.

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

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

$$-3x-x^{2}=0$$

Tauwehea te x.

$$x\left(-3-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -3-x=0.

$$x=0 x=-3$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-3\right)^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-3x,x,x^{2}-6x+9.

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

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

$$3x-9+\left(x-3\right)^{2}=x\times 2x$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-3\right)^{2}.

$$3x-9+x^{2}-6x+9=x\times 2x$$

Pahekotia te 3x me -6x, ka -3x.

$$-3x-9+x^{2}+9=x\times 2x$$

Tāpirihia te -9 ki te 9, ka 0.

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

Whakareatia te x ki te x, ka x^{2}.

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

Tangohia te x^{2}\times 2 mai i ngā taha e rua.

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

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

$$-3x-x^{2}=0$$

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.

$$-x^{2}-3x=0$$

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

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

Tuhia te pūtakerua o te \left(-3\right)^{2}.

$$x=\frac{-\left(-3\right)±3}{2\left(-1\right)}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±3}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{3±3}{-2}$$

Nā, me whakaoti te whārite x=\frac{3±3}{-2} ina he tāpiri te ±. Tāpiri 3 ki te 3.

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

Whakawehe 6 ki te -2.

$$x=-3$$

Nā, me whakaoti te whārite x=\frac{3±3}{-2} ina he tango te ±. Tango 3 mai i 3.

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

Whakawehe 0 ki te -2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-3 x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-3\right)^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-3x,x,x^{2}-6x+9.

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

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

$$3x-9+\left(x-3\right)^{2}=x\times 2x$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-3\right)^{2}.

$$3x-9+x^{2}-6x+9=x\times 2x$$

Pahekotia te 3x me -6x, ka -3x.

$$-3x-9+x^{2}+9=x\times 2x$$

Tāpirihia te -9 ki te 9, ka 0.

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

Whakareatia te x ki te x, ka x^{2}.

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

Tangohia te x^{2}\times 2 mai i ngā taha e rua.

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

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

$$-3x-x^{2}=0$$

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.

$$-x^{2}-3x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-3x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\left(-\frac{3}{-1}\right)x=\frac{0}{-1}$$

Whakawehe -3 ki te -1.

$$x^{2}+3x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}+3x=0$$

Whakawehea te 3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{2}. Nā, tāpiria te pūrua o te \frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia \frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+3x+\frac{9}{4}=\frac{9}{4}$$

Tauwehea x^{2}+3x+\frac{9}{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}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

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

Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.

$$x=0 x=-3$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-3$$