Whakaoti i te 1/frac{1{x-10}-1/x}=720

$$\frac{ 1 }{ \frac{ 1 }{ x-10 } - \frac{ 1 }{ x } } = 720$$

Whakaoti mō x

$$x=-80$$

$$x=90$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o x-10 me x ko x\left(x-10\right). Whakareatia \frac{1}{x-10} ki te \frac{x}{x}. Whakareatia \frac{1}{x} ki te \frac{x-10}{x-10}.

$$\frac{1}{\frac{x}{x\left(x-10\right)}-\frac{x-10}{x\left(x-10\right)}}=720$$

Tā te mea he rite te tauraro o \frac{x}{x\left(x-10\right)} me \frac{x-10}{x\left(x-10\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{\frac{x-\left(x-10\right)}{x\left(x-10\right)}}=720$$

Mahia ngā whakarea i roto o x-\left(x-10\right).

$$\frac{1}{\frac{x-x+10}{x\left(x-10\right)}}=720$$

Whakakotahitia ngā kupu rite i x-x+10.

$$\frac{1}{\frac{10}{x\left(x-10\right)}}=720$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,10 nā te kore tautuhi i te whakawehenga mā te kore. Whakawehe 1 ki te \frac{10}{x\left(x-10\right)} mā te whakarea 1 ki te tau huripoki o \frac{10}{x\left(x-10\right)}.

$$\frac{x\left(x-10\right)}{10}=720$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-10.

$$\frac{x^{2}-10x}{10}=720$$

Whakawehea ia wā o x^{2}-10x ki te 10, kia riro ko \frac{1}{10}x^{2}-x.

$$\frac{1}{10}x^{2}-x=720$$

Tangohia te 720 mai i ngā taha e rua.

$$\frac{1}{10}x^{2}-x-720=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{10} mō a, -1 mō b, me -720 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times \frac{1}{10}\left(-720\right)}}{2\times \frac{1}{10}}$$

Whakareatia -4 ki te \frac{1}{10}.

$$x=\frac{-\left(-1\right)±\sqrt{1-\frac{2}{5}\left(-720\right)}}{2\times \frac{1}{10}}$$

Whakareatia -\frac{2}{5} ki te -720.

$$x=\frac{-\left(-1\right)±\sqrt{1+288}}{2\times \frac{1}{10}}$$

Tāpiri 1 ki te 288.

$$x=\frac{-\left(-1\right)±\sqrt{289}}{2\times \frac{1}{10}}$$

Tuhia te pūtakerua o te 289.

$$x=\frac{-\left(-1\right)±17}{2\times \frac{1}{10}}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±17}{2\times \frac{1}{10}}$$

Whakareatia 2 ki te \frac{1}{10}.

$$x=\frac{1±17}{\frac{1}{5}}$$

Nā, me whakaoti te whārite x=\frac{1±17}{\frac{1}{5}} ina he tāpiri te ±. Tāpiri 1 ki te 17.

$$x=\frac{18}{\frac{1}{5}}$$

Whakawehe 18 ki te \frac{1}{5} mā te whakarea 18 ki te tau huripoki o \frac{1}{5}.

$$x=90$$

Nā, me whakaoti te whārite x=\frac{1±17}{\frac{1}{5}} ina he tango te ±. Tango 17 mai i 1.

$$x=-\frac{16}{\frac{1}{5}}$$

Whakawehe -16 ki te \frac{1}{5} mā te whakarea -16 ki te tau huripoki o \frac{1}{5}.

$$x=-80$$

Kua oti te whārite te whakatau.

$$x=90 x=-80$$

Ngā Upane mō te Whakaoti i te Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o x-10 me x ko x\left(x-10\right). Whakareatia \frac{1}{x-10} ki te \frac{x}{x}. Whakareatia \frac{1}{x} ki te \frac{x-10}{x-10}.

$$\frac{1}{\frac{x}{x\left(x-10\right)}-\frac{x-10}{x\left(x-10\right)}}=720$$

Tā te mea he rite te tauraro o \frac{x}{x\left(x-10\right)} me \frac{x-10}{x\left(x-10\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{\frac{x-\left(x-10\right)}{x\left(x-10\right)}}=720$$

Mahia ngā whakarea i roto o x-\left(x-10\right).

$$\frac{1}{\frac{x-x+10}{x\left(x-10\right)}}=720$$

Whakakotahitia ngā kupu rite i x-x+10.

$$\frac{1}{\frac{10}{x\left(x-10\right)}}=720$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,10 nā te kore tautuhi i te whakawehenga mā te kore. Whakawehe 1 ki te \frac{10}{x\left(x-10\right)} mā te whakarea 1 ki te tau huripoki o \frac{10}{x\left(x-10\right)}.

$$\frac{x\left(x-10\right)}{10}=720$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-10.

$$\frac{x^{2}-10x}{10}=720$$

Whakawehea ia wā o x^{2}-10x ki te 10, kia riro ko \frac{1}{10}x^{2}-x.

$$\frac{1}{10}x^{2}-x=720$$

Me whakarea ngā taha e rua ki te 10.

$$\frac{\frac{1}{10}x^{2}-x}{\frac{1}{10}}=\frac{720}{\frac{1}{10}}$$

Mā te whakawehe ki te \frac{1}{10} ka wetekia te whakareanga ki te \frac{1}{10}.

$$x^{2}+\left(-\frac{1}{\frac{1}{10}}\right)x=\frac{720}{\frac{1}{10}}$$

Whakawehe -1 ki te \frac{1}{10} mā te whakarea -1 ki te tau huripoki o \frac{1}{10}.

$$x^{2}-10x=\frac{720}{\frac{1}{10}}$$

Whakawehe 720 ki te \frac{1}{10} mā te whakarea 720 ki te tau huripoki o \frac{1}{10}.

$$x^{2}-10x=7200$$

Whakawehea te -10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -5. Nā, tāpiria te pūrua o te -5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-10x+\left(-5\right)^{2}=7200+\left(-5\right)^{2}$$

Pūrua -5.

$$x^{2}-10x+25=7200+25$$

Tāpiri 7200 ki te 25.

$$x^{2}-10x+25=7225$$

Tauwehea x^{2}-10x+25. 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}.

$$\left(x-5\right)^{2}=7225$$

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

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{7225}$$

Whakarūnātia.

$$x-5=85 x-5=-85$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x=90 x=-80$$