Whakaoti i te 3x/x+1+6/2x=7/x

$$\frac { 3 x } { x + 1 } + \frac { 6 } { 2 x } = \frac { 7 } { x }$$

Whakaoti mō x

$$x=-\frac{2}{3}\approx -0.666666667$$

$$x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,0 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 x+1,2x,x.

$$2x\times 3x+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

Whakareatia te 2 ki te 3, ka 6.

$$6xx+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

Whakareatia te x ki te x, ka x^{2}.

$$6x^{2}+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+1 ki te 6.

$$6x^{2}+6x+6=\left(2x+2\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+2 ki te 7.

$$6x^{2}+6x+6=14x+14$$

Tangohia te 14x mai i ngā taha e rua.

$$6x^{2}+6x+6-14x=14$$

Pahekotia te 6x me -14x, ka -8x.

$$6x^{2}-8x+6=14$$

Tangohia te 14 mai i ngā taha e rua.

$$6x^{2}-8x+6-14=0$$

Tangohia te 14 i te 6, ka -8.

$$6x^{2}-8x-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -8 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 6\left(-8\right)}}{2\times 6}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 6\left(-8\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-8\right)±\sqrt{64-24\left(-8\right)}}{2\times 6}$$

Whakareatia -24 ki te -8.

$$x=\frac{-\left(-8\right)±\sqrt{64+192}}{2\times 6}$$

Tāpiri 64 ki te 192.

$$x=\frac{-\left(-8\right)±\sqrt{256}}{2\times 6}$$

Tuhia te pūtakerua o te 256.

$$x=\frac{-\left(-8\right)±16}{2\times 6}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±16}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{8±16}{12}$$

Nā, me whakaoti te whārite x=\frac{8±16}{12} ina he tāpiri te ±. Tāpiri 8 ki te 16.

$$x=\frac{24}{12}$$

Whakawehe 24 ki te 12.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{8±16}{12} ina he tango te ±. Tango 16 mai i 8.

$$x=-\frac{8}{12}$$

Whakahekea te hautanga \frac{-8}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,0 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 x+1,2x,x.

$$2x\times 3x+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

Whakareatia te 2 ki te 3, ka 6.

$$6xx+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

Whakareatia te x ki te x, ka x^{2}.

$$6x^{2}+\left(x+1\right)\times 6=\left(2x+2\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+1 ki te 6.

$$6x^{2}+6x+6=\left(2x+2\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+2 ki te 7.

$$6x^{2}+6x+6=14x+14$$

Tangohia te 14x mai i ngā taha e rua.

$$6x^{2}+6x+6-14x=14$$

Pahekotia te 6x me -14x, ka -8x.

$$6x^{2}-8x+6=14$$

Tangohia te 6 mai i ngā taha e rua.

$$6x^{2}-8x=14-6$$

Tangohia te 6 i te 14, ka 8.

$$6x^{2}-8x=8$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-8x}{6}=\frac{8}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\left(-\frac{8}{6}\right)x=\frac{8}{6}$$

Whakahekea te hautanga \frac{-8}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{4}{3}x=\frac{8}{6}$$

Whakahekea te hautanga \frac{8}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{4}{3}x=\frac{4}{3}$$

Whakawehea te -\frac{4}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{2}{3}. Nā, tāpiria te pūrua o te -\frac{2}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{2}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

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

Tāpiri \frac{4}{3} ki te \frac{4}{9} 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.

$$x^{2}-\frac{4}{3}x+\frac{4}{9}=\frac{16}{9}$$

Tauwehea x^{2}-\frac{4}{3}x+\frac{4}{9}. 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}.

$$\left(x-\frac{2}{3}\right)^{2}=\frac{16}{9}$$

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

$$\sqrt{\left(x-\frac{2}{3}\right)^{2}}=\sqrt{\frac{16}{9}}$$

Whakarūnātia.

$$x-\frac{2}{3}=\frac{4}{3} x-\frac{2}{3}=-\frac{4}{3}$$

Me tāpiri \frac{2}{3} ki ngā taha e rua o te whārite.

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