Whakaoti i te x=6/x-6

$$x= \frac{ 6 }{ x-6 }$$

Whakaoti mō x

$$x=\sqrt{15}+3\approx 6.872983346$$

$$x=3-\sqrt{15}\approx -0.872983346$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te \frac{6}{x-6} mai i ngā taha e rua.

$$x-\frac{6}{x-6}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{x-6}{x-6}.

$$\frac{x\left(x-6\right)}{x-6}-\frac{6}{x-6}=0$$

Tā te mea he rite te tauraro o \frac{x\left(x-6\right)}{x-6} me \frac{6}{x-6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\left(x-6\right)-6}{x-6}=0$$

Mahia ngā whakarea i roto o x\left(x-6\right)-6.

$$\frac{x^{2}-6x-6}{x-6}=0$$

Tē taea kia ōrite te tāupe x ki 6 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x-6.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -6 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-6\right)}}{2}$$

Whakareatia -4 ki te -6.

$$x=\frac{-\left(-6\right)±\sqrt{36+24}}{2}$$

Tāpiri 36 ki te 24.

$$x=\frac{-\left(-6\right)±\sqrt{60}}{2}$$

Tuhia te pūtakerua o te 60.

$$x=\frac{-\left(-6\right)±2\sqrt{15}}{2}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±2\sqrt{15}}{2}$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{15}}{2} ina he tāpiri te ±. Tāpiri 6 ki te 2\sqrt{15}.

$$x=\frac{2\sqrt{15}+6}{2}$$

Whakawehe 6+2\sqrt{15} ki te 2.

$$x=\sqrt{15}+3$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{15}}{2} ina he tango te ±. Tango 2\sqrt{15} mai i 6.

$$x=\frac{6-2\sqrt{15}}{2}$$

Whakawehe 6-2\sqrt{15} ki te 2.

$$x=3-\sqrt{15}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{15}+3 x=3-\sqrt{15}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te \frac{6}{x-6} mai i ngā taha e rua.

$$x-\frac{6}{x-6}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{x-6}{x-6}.

$$\frac{x\left(x-6\right)}{x-6}-\frac{6}{x-6}=0$$

Tā te mea he rite te tauraro o \frac{x\left(x-6\right)}{x-6} me \frac{6}{x-6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\left(x-6\right)-6}{x-6}=0$$

Mahia ngā whakarea i roto o x\left(x-6\right)-6.

$$\frac{x^{2}-6x-6}{x-6}=0$$

Tē taea kia ōrite te tāupe x ki 6 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x-6.

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

Me tāpiri te 6 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

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

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

Pūrua -3.

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

Tāpiri 6 ki te 9.

$$x^{2}-6x+9=15$$

Tauwehea x^{2}-6x+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}.

$$\left(x-3\right)^{2}=15$$

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

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{15}$$

Whakarūnātia.

$$x-3=\sqrt{15} x-3=-\sqrt{15}$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=\sqrt{15}+3 x=3-\sqrt{15}$$