Whakaoti i te 3x/+4-5-x/x+1=2

$$\frac { 3 x } { + 4 } - \frac { 5 - x } { x + 1 } = 2$$

Whakaoti mō x

$$x = \frac{\sqrt{337} + 1}{6} \approx 3.226259958$$

$$x=\frac{1-\sqrt{337}}{6}\approx -2.892926625$$

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. Me whakarea ngā taha e rua o te whārite ki te 4\left(x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 4,x+1.

$$\left(x+1\right)\times 3x-4\left(5-x\right)=8\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+1 ki te 3.

$$\left(3x+3\right)x-4\left(5-x\right)=8\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x+3 ki te x.

$$3x^{2}+3x-4\left(5-x\right)=8\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -4 ki te 5-x.

$$3x^{2}+3x-20+4x=8\left(x+1\right)$$

Pahekotia te 3x me 4x, ka 7x.

$$3x^{2}+7x-20=8\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8 ki te x+1.

$$3x^{2}+7x-20=8x+8$$

Tangohia te 8x mai i ngā taha e rua.

$$3x^{2}+7x-20-8x=8$$

Pahekotia te 7x me -8x, ka -x.

$$3x^{2}-x-20=8$$

Tangohia te 8 mai i ngā taha e rua.

$$3x^{2}-x-20-8=0$$

Tangohia te 8 i te -20, ka -28.

$$3x^{2}-x-28=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -1 mō b, me -28 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 3\left(-28\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-1\right)±\sqrt{1-12\left(-28\right)}}{2\times 3}$$

Whakareatia -12 ki te -28.

$$x=\frac{-\left(-1\right)±\sqrt{1+336}}{2\times 3}$$

Tāpiri 1 ki te 336.

$$x=\frac{-\left(-1\right)±\sqrt{337}}{2\times 3}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{337}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{1±\sqrt{337}}{6}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{337}}{6} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{337}.

$$x=\frac{\sqrt{337}+1}{6}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{337}}{6} ina he tango te ±. Tango \sqrt{337} mai i 1.

$$x=\frac{1-\sqrt{337}}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{337}+1}{6} x=\frac{1-\sqrt{337}}{6}$$

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. Me whakarea ngā taha e rua o te whārite ki te 4\left(x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 4,x+1.

$$\left(x+1\right)\times 3x-4\left(5-x\right)=8\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+1 ki te 3.

$$\left(3x+3\right)x-4\left(5-x\right)=8\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x+3 ki te x.

$$3x^{2}+3x-4\left(5-x\right)=8\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -4 ki te 5-x.

$$3x^{2}+3x-20+4x=8\left(x+1\right)$$

Pahekotia te 3x me 4x, ka 7x.

$$3x^{2}+7x-20=8\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8 ki te x+1.

$$3x^{2}+7x-20=8x+8$$

Tangohia te 8x mai i ngā taha e rua.

$$3x^{2}+7x-20-8x=8$$

Pahekotia te 7x me -8x, ka -x.

$$3x^{2}-x-20=8$$

Me tāpiri te 20 ki ngā taha e rua.

$$3x^{2}-x=8+20$$

Tāpirihia te 8 ki te 20, ka 28.

$$3x^{2}-x=28$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-x}{3}=\frac{28}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}-\frac{1}{3}x=\frac{28}{3}$$

Whakawehea te -\frac{1}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{6}. Nā, tāpiria te pūrua o te -\frac{1}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{3}x+\left(-\frac{1}{6}\right)^{2}=\frac{28}{3}+\left(-\frac{1}{6}\right)^{2}$$

Pūruatia -\frac{1}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{28}{3}+\frac{1}{36}$$

Tāpiri \frac{28}{3} ki te \frac{1}{36} 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.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{337}{36}$$

Tauwehea x^{2}-\frac{1}{3}x+\frac{1}{36}. 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}.

$$\left(x-\frac{1}{6}\right)^{2}=\frac{337}{36}$$

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

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{\frac{337}{36}}$$

Whakarūnātia.

$$x-\frac{1}{6}=\frac{\sqrt{337}}{6} x-\frac{1}{6}=-\frac{\sqrt{337}}{6}$$

Me tāpiri \frac{1}{6} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{337}+1}{6} x=\frac{1-\sqrt{337}}{6}$$