Whakaoti i te 4x/2x-21/2x-2=1

$$\frac { 4 x } { 2 x } - \frac { 21 } { 2 x - 2 } = 1$$

Whakaoti mō x

$$x = \frac{23}{2} = 11\frac{1}{2} = 11.5$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x,2x-2.

$$\left(x-1\right)\times 4x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-1 ki te 4.

$$\left(4x-4\right)x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-4 ki te x.

$$4x^{2}-4x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-1.

$$4x^{2}-4x-x\times 21=2x^{2}-2x$$

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

$$4x^{2}-4x-x\times 21-2x^{2}=-2x$$

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

$$2x^{2}-4x-x\times 21=-2x$$

Me tāpiri te 2x ki ngā taha e rua.

$$2x^{2}-4x-x\times 21+2x=0$$

Pahekotia te -4x me 2x, ka -2x.

$$2x^{2}-2x-x\times 21=0$$

Whakareatia te -1 ki te 21, ka -21.

$$2x^{2}-2x-21x=0$$

Pahekotia te -2x me -21x, ka -23x.

$$2x^{2}-23x=0$$

Tauwehea te x.

$$x\left(2x-23\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 2x-23=0.

$$x=0 x=\frac{23}{2}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{23}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x,2x-2.

$$\left(x-1\right)\times 4x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-1 ki te 4.

$$\left(4x-4\right)x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-4 ki te x.

$$4x^{2}-4x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-1.

$$4x^{2}-4x-x\times 21=2x^{2}-2x$$

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

$$4x^{2}-4x-x\times 21-2x^{2}=-2x$$

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

$$2x^{2}-4x-x\times 21=-2x$$

Me tāpiri te 2x ki ngā taha e rua.

$$2x^{2}-4x-x\times 21+2x=0$$

Pahekotia te -4x me 2x, ka -2x.

$$2x^{2}-2x-x\times 21=0$$

Whakareatia te -1 ki te 21, ka -21.

$$2x^{2}-2x-21x=0$$

Pahekotia te -2x me -21x, ka -23x.

$$2x^{2}-23x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -23 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-23\right)±\sqrt{\left(-23\right)^{2}}}{2\times 2}$$

Tuhia te pūtakerua o te \left(-23\right)^{2}.

$$x=\frac{-\left(-23\right)±23}{2\times 2}$$

Ko te tauaro o -23 ko 23.

$$x=\frac{23±23}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{23±23}{4}$$

Nā, me whakaoti te whārite x=\frac{23±23}{4} ina he tāpiri te ±. Tāpiri 23 ki te 23.

$$x=\frac{46}{4}$$

Whakahekea te hautanga \frac{46}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{23}{2}$$

Nā, me whakaoti te whārite x=\frac{23±23}{4} ina he tango te ±. Tango 23 mai i 23.

$$x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{23}{2} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{23}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x,2x-2.

$$\left(x-1\right)\times 4x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-1 ki te 4.

$$\left(4x-4\right)x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-4 ki te x.

$$4x^{2}-4x-x\times 21=2x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-1.

$$4x^{2}-4x-x\times 21=2x^{2}-2x$$

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

$$4x^{2}-4x-x\times 21-2x^{2}=-2x$$

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

$$2x^{2}-4x-x\times 21=-2x$$

Me tāpiri te 2x ki ngā taha e rua.

$$2x^{2}-4x-x\times 21+2x=0$$

Pahekotia te -4x me 2x, ka -2x.

$$2x^{2}-2x-x\times 21=0$$

Whakareatia te -1 ki te 21, ka -21.

$$2x^{2}-2x-21x=0$$

Pahekotia te -2x me -21x, ka -23x.

$$2x^{2}-23x=0$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-23x}{2}=\frac{0}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}-\frac{23}{2}x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x^{2}-\frac{23}{2}x=0$$

Whakawehea te -\frac{23}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{23}{4}. Nā, tāpiria te pūrua o te -\frac{23}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{23}{2}x+\left(-\frac{23}{4}\right)^{2}=\left(-\frac{23}{4}\right)^{2}$$

Pūruatia -\frac{23}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{23}{2}x+\frac{529}{16}=\frac{529}{16}$$

Tauwehea x^{2}-\frac{23}{2}x+\frac{529}{16}. 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}.

$$\left(x-\frac{23}{4}\right)^{2}=\frac{529}{16}$$

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

$$\sqrt{\left(x-\frac{23}{4}\right)^{2}}=\sqrt{\frac{529}{16}}$$

Whakarūnātia.

$$x-\frac{23}{4}=\frac{23}{4} x-\frac{23}{4}=-\frac{23}{4}$$

Me tāpiri \frac{23}{4} ki ngā taha e rua o te whārite.

$$x=\frac{23}{2} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{23}{2}$$