Whakaoti i te x-1/2x+3-2x-1/3-2x=0

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

Whakaoti mō x

$$x=\frac{1}{6}\approx 0.166666667$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

$$\left(2x-3\right)\left(x-1\right)-\left(-3-2x\right)\left(2x-1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-3 ki te x-1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x+3-\left(-3-2x\right)\left(2x-1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -3-2x ki te 2x-1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x+3-\left(-4x+3-4x^{2}\right)=0$$

Hei kimi i te tauaro o -4x+3-4x^{2}, kimihia te tauaro o ia taurangi.

$$2x^{2}-5x+3+4x-3+4x^{2}=0$$

Pahekotia te -5x me 4x, ka -x.

$$2x^{2}-x+3-3+4x^{2}=0$$

Tangohia te 3 i te 3, ka 0.

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

Pahekotia te 2x^{2} me 4x^{2}, ka 6x^{2}.

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

Tauwehea te x.

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

Hei kimi otinga whārite, me whakaoti te x=0 me te 6x-1=0.

$$x=0 x=\frac{1}{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$\left(2x-3\right)\left(x-1\right)-\left(-3-2x\right)\left(2x-1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-3 ki te x-1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x+3-\left(-3-2x\right)\left(2x-1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -3-2x ki te 2x-1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x+3-\left(-4x+3-4x^{2}\right)=0$$

Hei kimi i te tauaro o -4x+3-4x^{2}, kimihia te tauaro o ia taurangi.

$$2x^{2}-5x+3+4x-3+4x^{2}=0$$

Pahekotia te -5x me 4x, ka -x.

$$2x^{2}-x+3-3+4x^{2}=0$$

Tangohia te 3 i te 3, ka 0.

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

Pahekotia te 2x^{2} me 4x^{2}, ka 6x^{2}.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -1 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 6}$$

Tuhia te pūtakerua o te 1.

$$x=\frac{-\left(-1\right)±1}{2\times 6}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±1}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{1±1}{12}$$

Nā, me whakaoti te whārite x=\frac{1±1}{12} ina he tāpiri te ±. Tāpiri 1 ki te 1.

$$x=\frac{2}{12}$$

Whakahekea te hautanga \frac{2}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{1}{6}$$

Nā, me whakaoti te whārite x=\frac{1±1}{12} ina he tango te ±. Tango 1 mai i 1.

$$x=\frac{0}{12}$$

Whakawehe 0 ki te 12.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{6} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$\left(2x-3\right)\left(x-1\right)-\left(-3-2x\right)\left(2x-1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-3 ki te x-1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x+3-\left(-3-2x\right)\left(2x-1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -3-2x ki te 2x-1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x+3-\left(-4x+3-4x^{2}\right)=0$$

Hei kimi i te tauaro o -4x+3-4x^{2}, kimihia te tauaro o ia taurangi.

$$2x^{2}-5x+3+4x-3+4x^{2}=0$$

Pahekotia te -5x me 4x, ka -x.

$$2x^{2}-x+3-3+4x^{2}=0$$

Tangohia te 3 i te 3, ka 0.

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

Pahekotia te 2x^{2} me 4x^{2}, ka 6x^{2}.

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

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-x}{6}=\frac{0}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}-\frac{1}{6}x=\frac{0}{6}$$

Whakawehe 0 ki te 6.

$$x^{2}-\frac{1}{6}x=0$$

Whakawehea te -\frac{1}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{12}. Nā, tāpiria te pūrua o te -\frac{1}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{6}x+\left(-\frac{1}{12}\right)^{2}=\left(-\frac{1}{12}\right)^{2}$$

Pūruatia -\frac{1}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{6}x+\frac{1}{144}=\frac{1}{144}$$

Tauwehea x^{2}-\frac{1}{6}x+\frac{1}{144}. 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}.

$$\left(x-\frac{1}{12}\right)^{2}=\frac{1}{144}$$

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

$$\sqrt{\left(x-\frac{1}{12}\right)^{2}}=\sqrt{\frac{1}{144}}$$

Whakarūnātia.

$$x-\frac{1}{12}=\frac{1}{12} x-\frac{1}{12}=-\frac{1}{12}$$

Me tāpiri \frac{1}{12} ki ngā taha e rua o te whārite.

$$x=\frac{1}{6} x=0$$