Whakaoti i te (1/xdiv2)+1/x=1/16

$$( \frac{ 1 }{ x } \div 2)+ \frac{ 1 }{ x } = \frac{ 1 }{ 16 }$$

Whakaoti mō x

$$x=24$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 16x, arā, te tauraro pātahi he tino iti rawa te kitea o 2,x,16.

$$8x\times \frac{1}{x}+16=x$$

Tuhia te 8\times \frac{1}{x} hei hautanga kotahi.

$$\frac{8}{x}x+16=x$$

Tuhia te \frac{8}{x}x hei hautanga kotahi.

$$\frac{8x}{x}+16=x$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 16 ki te \frac{x}{x}.

$$\frac{8x}{x}+\frac{16x}{x}=x$$

Tā te mea he rite te tauraro o \frac{8x}{x} me \frac{16x}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x+16x}{x}=x$$

Whakakotahitia ngā kupu rite i 8x+16x.

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

Tangohia te x mai i ngā taha e rua.

$$\frac{24x}{x}-x=0$$

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

$$\frac{24x}{x}-\frac{xx}{x}=0$$

Tā te mea he rite te tauraro o \frac{24x}{x} me \frac{xx}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{24x-xx}{x}=0$$

Mahia ngā whakarea i roto o 24x-xx.

$$\frac{24x-x^{2}}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$24x-x^{2}=0$$

Tauwehea te x.

$$x\left(24-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 24-x=0.

$$x=0 x=24$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=24$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 16x, arā, te tauraro pātahi he tino iti rawa te kitea o 2,x,16.

$$8x\times \frac{1}{x}+16=x$$

Tuhia te 8\times \frac{1}{x} hei hautanga kotahi.

$$\frac{8}{x}x+16=x$$

Tuhia te \frac{8}{x}x hei hautanga kotahi.

$$\frac{8x}{x}+16=x$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 16 ki te \frac{x}{x}.

$$\frac{8x}{x}+\frac{16x}{x}=x$$

Tā te mea he rite te tauraro o \frac{8x}{x} me \frac{16x}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x+16x}{x}=x$$

Whakakotahitia ngā kupu rite i 8x+16x.

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

Tangohia te x mai i ngā taha e rua.

$$\frac{24x}{x}-x=0$$

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

$$\frac{24x}{x}-\frac{xx}{x}=0$$

Tā te mea he rite te tauraro o \frac{24x}{x} me \frac{xx}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{24x-xx}{x}=0$$

Mahia ngā whakarea i roto o 24x-xx.

$$\frac{24x-x^{2}}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$24x-x^{2}=0$$

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.

$$-x^{2}+24x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 24 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-24±\sqrt{24^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 24^{2}.

$$x=\frac{-24±24}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-24±24}{-2}$$

Nā, me whakaoti te whārite x=\frac{-24±24}{-2} ina he tāpiri te ±. Tāpiri -24 ki te 24.

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

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-24±24}{-2} ina he tango te ±. Tango 24 mai i -24.

$$x=-\frac{48}{-2}$$

Whakawehe -48 ki te -2.

$$x=24$$

Kua oti te whārite te whakatau.

$$x=0 x=24$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=24$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 16x, arā, te tauraro pātahi he tino iti rawa te kitea o 2,x,16.

$$8x\times \frac{1}{x}+16=x$$

Tuhia te 8\times \frac{1}{x} hei hautanga kotahi.

$$\frac{8}{x}x+16=x$$

Tuhia te \frac{8}{x}x hei hautanga kotahi.

$$\frac{8x}{x}+16=x$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 16 ki te \frac{x}{x}.

$$\frac{8x}{x}+\frac{16x}{x}=x$$

Tā te mea he rite te tauraro o \frac{8x}{x} me \frac{16x}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x+16x}{x}=x$$

Whakakotahitia ngā kupu rite i 8x+16x.

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

Tangohia te x mai i ngā taha e rua.

$$\frac{24x}{x}-x=0$$

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

$$\frac{24x}{x}-\frac{xx}{x}=0$$

Tā te mea he rite te tauraro o \frac{24x}{x} me \frac{xx}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{24x-xx}{x}=0$$

Mahia ngā whakarea i roto o 24x-xx.

$$\frac{24x-x^{2}}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$24x-x^{2}=0$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-x^{2}+24x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+24x}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{24}{-1}x=\frac{0}{-1}$$

Whakawehe 24 ki te -1.

$$x^{2}-24x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}-24x=0$$

Whakawehea te -24, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -12. Nā, tāpiria te pūrua o te -12 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-24x+\left(-12\right)^{2}=\left(-12\right)^{2}$$

Pūrua -12.

$$x^{2}-24x+144=144$$

Tauwehea x^{2}-24x+144. 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}.

$$\left(x-12\right)^{2}=144$$

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

$$\sqrt{\left(x-12\right)^{2}}=\sqrt{144}$$

Whakarūnātia.

$$x-12=12 x-12=-12$$

Me tāpiri 12 ki ngā taha e rua o te whārite.

$$x=24 x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=24$$