Whakaoti i te 4x-1/x+1=x-1

$$\frac { 4 x - 1 } { x + 1 } = x - 1$$

Whakaoti mō x

$$x=4$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+1.

$$4x-1=\left(x+1\right)x+\left(x+1\right)\left(-1\right)$$

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

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

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

$$4x-1=x^{2}+x-x-1$$

Pahekotia te x me -x, ka 0.

$$4x-1=x^{2}-1$$

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

$$4x-1-x^{2}=-1$$

Me tāpiri te 1 ki ngā taha e rua.

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

Tāpirihia te -1 ki te 1, ka 0.

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

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.

$$x=0 x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+1.

$$4x-1=\left(x+1\right)x+\left(x+1\right)\left(-1\right)$$

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

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

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

$$4x-1=x^{2}+x-x-1$$

Pahekotia te x me -x, ka 0.

$$4x-1=x^{2}-1$$

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

$$4x-1-x^{2}=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$4x-x^{2}=-1+1$$

Tāpirihia te -1 ki te 1, ka 0.

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

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 x^{2}-4x+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}.

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

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.

$$x=4 x=0$$