Whakaoti i te 2x-9/x+4=3x-6/x+4

$$2 x - \frac { 9 } { x + 4 } = \frac { 3 x - 6 } { x + 4 }$$

Whakaoti mō x

$$x=-3$$

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+4.

$$2x\left(x+4\right)-9=3x-6$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x+4.

$$2x^{2}+8x-9=3x-6$$

Tangohia te 3x mai i ngā taha e rua.

$$2x^{2}+8x-9-3x=-6$$

Pahekotia te 8x me -3x, ka 5x.

$$2x^{2}+5x-9=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$2x^{2}+5x-9+6=0$$

Tāpirihia te -9 ki te 6, ka -3.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 5 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\times 2\left(-3\right)}}{2\times 2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\times 2\left(-3\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-5±\sqrt{25-8\left(-3\right)}}{2\times 2}$$

Whakareatia -8 ki te -3.

$$x=\frac{-5±\sqrt{25+24}}{2\times 2}$$

Tāpiri 25 ki te 24.

$$x=\frac{-5±\sqrt{49}}{2\times 2}$$

Tuhia te pūtakerua o te 49.

$$x=\frac{-5±7}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-5±7}{4}$$

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

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

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

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

Whakawehe -12 ki te 4.

$$x=-3$$

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+4.

$$2x\left(x+4\right)-9=3x-6$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x+4.

$$2x^{2}+8x-9=3x-6$$

Tangohia te 3x mai i ngā taha e rua.

$$2x^{2}+8x-9-3x=-6$$

Pahekotia te 8x me -3x, ka 5x.

$$2x^{2}+5x-9=-6$$

Me tāpiri te 9 ki ngā taha e rua.

$$2x^{2}+5x=-6+9$$

Tāpirihia te -6 ki te 9, ka 3.

$$2x^{2}+5x=3$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+5x}{2}=\frac{3}{2}$$

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

$$x^{2}+\frac{5}{2}x=\frac{3}{2}$$

Whakawehea te \frac{5}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{4}. Nā, tāpiria te pūrua o te \frac{5}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia \frac{5}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{3}{2}+\frac{25}{16}$$

Tāpiri \frac{3}{2} ki te \frac{25}{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.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{49}{16}$$

Tauwehea x^{2}+\frac{5}{2}x+\frac{25}{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}.

$$\left(x+\frac{5}{4}\right)^{2}=\frac{49}{16}$$

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

$$\sqrt{\left(x+\frac{5}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Whakarūnātia.

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

Me tango \frac{5}{4} mai i ngā taha e rua o te whārite.

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