Whakaoti i te 36/x(x-12)-3/x-12=3

$$\frac { 36 } { x ( x - 12 ) } - \frac { 3 } { x - 12 } = 3$$

Whakaoti mō x

$$x=-1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,12 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-12\right), arā, te tauraro pātahi he tino iti rawa te kitea o x\left(x-12\right),x-12.

$$36-x\times 3=3x\left(x-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-12.

$$36-x\times 3=3x^{2}-36x$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$36-x\times 3-3x^{2}=-36x$$

Me tāpiri te 36x ki ngā taha e rua.

$$36-x\times 3-3x^{2}+36x=0$$

Whakareatia te -1 ki te 3, ka -3.

$$36-3x-3x^{2}+36x=0$$

Pahekotia te -3x me 36x, ka 33x.

$$36+33x-3x^{2}=0$$

Whakawehea ngā taha e rua ki te 3.

$$12+11x-x^{2}=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-x^{2}+11x+12=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=11 ab=-12=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$-1,12 -2,6 -3,4$$

Tātaihia te tapeke mō ia takirua.

$$-1+12=11 -2+6=4 -3+4=1$$

Ko te otinga te takirua ka hoatu i te tapeke 11.

$$a=12 b=-1$$

Tuhia anō te -x^{2}+11x+12 hei \left(-x^{2}+12x\right)+\left(-x+12\right).

$$\left(-x^{2}+12x\right)+\left(-x+12\right)$$

Tauwehea te -x i te tuatahi me te -1 i te rōpū tuarua.

$$-x\left(x-12\right)-\left(x-12\right)$$

Whakatauwehea atu te kīanga pātahi x-12 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-12\right)\left(-x-1\right)$$

Hei kimi otinga whārite, me whakaoti te x-12=0 me te -x-1=0.

$$x=12 x=-1$$

Tē taea kia ōrite te tāupe x ki 12.

$$x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,12 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-12\right), arā, te tauraro pātahi he tino iti rawa te kitea o x\left(x-12\right),x-12.

$$36-x\times 3=3x\left(x-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-12.

$$36-x\times 3=3x^{2}-36x$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$36-x\times 3-3x^{2}=-36x$$

Me tāpiri te 36x ki ngā taha e rua.

$$36-x\times 3-3x^{2}+36x=0$$

Whakareatia te -1 ki te 3, ka -3.

$$36-3x-3x^{2}+36x=0$$

Pahekotia te -3x me 36x, ka 33x.

$$36+33x-3x^{2}=0$$

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.

$$-3x^{2}+33x+36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 33 mō b, me 36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-33±\sqrt{33^{2}-4\left(-3\right)\times 36}}{2\left(-3\right)}$$

Pūrua 33.

$$x=\frac{-33±\sqrt{1089-4\left(-3\right)\times 36}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-33±\sqrt{1089+12\times 36}}{2\left(-3\right)}$$

Whakareatia 12 ki te 36.

$$x=\frac{-33±\sqrt{1089+432}}{2\left(-3\right)}$$

Tāpiri 1089 ki te 432.

$$x=\frac{-33±\sqrt{1521}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 1521.

$$x=\frac{-33±39}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{-33±39}{-6}$$

Nā, me whakaoti te whārite x=\frac{-33±39}{-6} ina he tāpiri te ±. Tāpiri -33 ki te 39.

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

Whakawehe 6 ki te -6.

$$x=-1$$

Nā, me whakaoti te whārite x=\frac{-33±39}{-6} ina he tango te ±. Tango 39 mai i -33.

$$x=-\frac{72}{-6}$$

Whakawehe -72 ki te -6.

$$x=12$$

Kua oti te whārite te whakatau.

$$x=-1 x=12$$

Tē taea kia ōrite te tāupe x ki 12.

$$x=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,12 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-12\right), arā, te tauraro pātahi he tino iti rawa te kitea o x\left(x-12\right),x-12.

$$36-x\times 3=3x\left(x-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-12.

$$36-x\times 3=3x^{2}-36x$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$36-x\times 3-3x^{2}=-36x$$

Me tāpiri te 36x ki ngā taha e rua.

$$36-x\times 3-3x^{2}+36x=0$$

Tangohia te 36 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-x\times 3-3x^{2}+36x=-36$$

Whakareatia te -1 ki te 3, ka -3.

$$-3x-3x^{2}+36x=-36$$

Pahekotia te -3x me 36x, ka 33x.

$$33x-3x^{2}=-36$$

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.

$$-3x^{2}+33x=-36$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}+33x}{-3}=-\frac{36}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$x^{2}+\frac{33}{-3}x=-\frac{36}{-3}$$

Whakawehe 33 ki te -3.

$$x^{2}-11x=-\frac{36}{-3}$$

Whakawehe -36 ki te -3.

$$x^{2}-11x=12$$

Whakawehea te -11, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{2}. Nā, tāpiria te pūrua o te -\frac{11}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-11x+\left(-\frac{11}{2}\right)^{2}=12+\left(-\frac{11}{2}\right)^{2}$$

Pūruatia -\frac{11}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-11x+\frac{121}{4}=12+\frac{121}{4}$$

Tāpiri 12 ki te \frac{121}{4}.

$$x^{2}-11x+\frac{121}{4}=\frac{169}{4}$$

Tauwehea te x^{2}-11x+\frac{121}{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}.

$$\left(x-\frac{11}{2}\right)^{2}=\frac{169}{4}$$

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

$$\sqrt{\left(x-\frac{11}{2}\right)^{2}}=\sqrt{\frac{169}{4}}$$

Whakarūnātia.

$$x-\frac{11}{2}=\frac{13}{2} x-\frac{11}{2}=-\frac{13}{2}$$

Me tāpiri \frac{11}{2} ki ngā taha e rua o te whārite.

$$x=12 x=-1$$

Tē taea kia ōrite te tāupe x ki 12.

$$x=-1$$