Whakaoti i te 2/x+1-2x=5

$$\frac{ 2 }{ x+1 } -2x=5$$

Whakaoti mō x

$$x=-\frac{1}{2}=-0.5$$

$$x=-3$$

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.

$$2-2x\left(x+1\right)=5\left(x+1\right)$$

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x+1.

$$2-2x^{2}-2x=5x+5$$

Tangohia te 5x mai i ngā taha e rua.

$$2-2x^{2}-2x-5x=5$$

Pahekotia te -2x me -5x, ka -7x.

$$2-2x^{2}-7x=5$$

Tangohia te 5 mai i ngā taha e rua.

$$2-2x^{2}-7x-5=0$$

Tangohia te 5 i te 2, ka -3.

$$-3-2x^{2}-7x=0$$

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.

$$-2x^{2}-7x-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, -7 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\left(-2\right)\left(-3\right)}}{2\left(-2\right)}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\left(-2\right)\left(-3\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-\left(-7\right)±\sqrt{49+8\left(-3\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -3.

$$x=\frac{-\left(-7\right)±\sqrt{49-24}}{2\left(-2\right)}$$

Tāpiri 49 ki te -24.

$$x=\frac{-\left(-7\right)±\sqrt{25}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-\left(-7\right)±5}{2\left(-2\right)}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±5}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{7±5}{-4}$$

Nā, me whakaoti te whārite x=\frac{7±5}{-4} ina he tāpiri te ±. Tāpiri 7 ki te 5.

$$x=\frac{12}{-4}$$

Whakawehe 12 ki te -4.

$$x=-3$$

Nā, me whakaoti te whārite x=\frac{7±5}{-4} ina he tango te ±. Tango 5 mai i 7.

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

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

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

Kua oti te whārite te whakatau.

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

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.

$$2-2x\left(x+1\right)=5\left(x+1\right)$$

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x+1.

$$2-2x^{2}-2x=5x+5$$

Tangohia te 5x mai i ngā taha e rua.

$$2-2x^{2}-2x-5x=5$$

Pahekotia te -2x me -5x, ka -7x.

$$2-2x^{2}-7x=5$$

Tangohia te 2 mai i ngā taha e rua.

$$-2x^{2}-7x=5-2$$

Tangohia te 2 i te 5, ka 3.

$$-2x^{2}-7x=3$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}-7x}{-2}=\frac{3}{-2}$$

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

$$x^{2}+\left(-\frac{7}{-2}\right)x=\frac{3}{-2}$$

Whakawehe -7 ki te -2.

$$x^{2}+\frac{7}{2}x=\frac{3}{-2}$$

Whakawehe 3 ki te -2.

$$x^{2}+\frac{7}{2}x=-\frac{3}{2}$$

Whakawehea te \frac{7}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{4}. Nā, tāpiria te pūrua o te \frac{7}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{7}{2}x+\left(\frac{7}{4}\right)^{2}=-\frac{3}{2}+\left(\frac{7}{4}\right)^{2}$$

Pūruatia \frac{7}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{7}{2}x+\frac{49}{16}=-\frac{3}{2}+\frac{49}{16}$$

Tāpiri -\frac{3}{2} ki te \frac{49}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{7}{2}x+\frac{49}{16}=\frac{25}{16}$$

Tauwehea x^{2}+\frac{7}{2}x+\frac{49}{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}.

$$\left(x+\frac{7}{4}\right)^{2}=\frac{25}{16}$$

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

$$\sqrt{\left(x+\frac{7}{4}\right)^{2}}=\sqrt{\frac{25}{16}}$$

Whakarūnātia.

$$x+\frac{7}{4}=\frac{5}{4} x+\frac{7}{4}=-\frac{5}{4}$$

Me tango \frac{7}{4} mai i ngā taha e rua o te whārite.

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