Whakaoti i te 36/x-6-36/x=1/5

$$\frac { 36 } { x - 6 } - \frac { 36 } { x } = \frac { 1 } { 5 }$$

Whakaoti mō x

$$x=-30$$

$$x=36$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,6 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 5x\left(x-6\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-6,x,5.

$$5x\times 36-\left(5x-30\right)\times 36=x\left(x-6\right)$$

Whakareatia te 5 ki te 36, ka 180.

$$180x-\left(5x-30\right)\times 36=x\left(x-6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5x-30 ki te 36.

$$180x-\left(180x-1080\right)=x\left(x-6\right)$$

Hei kimi i te tauaro o 180x-1080, kimihia te tauaro o ia taurangi.

$$180x-180x+1080=x\left(x-6\right)$$

Pahekotia te 180x me -180x, ka 0.

$$1080=x\left(x-6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-6.

$$1080=x^{2}-6x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-6x=1080$$

Tangohia te 1080 mai i ngā taha e rua.

$$x^{2}-6x-1080=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -6 mō b, me -1080 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1080\right)}}{2}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1080\right)}}{2}$$

Whakareatia -4 ki te -1080.

$$x=\frac{-\left(-6\right)±\sqrt{36+4320}}{2}$$

Tāpiri 36 ki te 4320.

$$x=\frac{-\left(-6\right)±\sqrt{4356}}{2}$$

Tuhia te pūtakerua o te 4356.

$$x=\frac{-\left(-6\right)±66}{2}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±66}{2}$$

Nā, me whakaoti te whārite x=\frac{6±66}{2} ina he tāpiri te ±. Tāpiri 6 ki te 66.

$$x=\frac{72}{2}$$

Whakawehe 72 ki te 2.

$$x=36$$

Nā, me whakaoti te whārite x=\frac{6±66}{2} ina he tango te ±. Tango 66 mai i 6.

$$x=-\frac{60}{2}$$

Whakawehe -60 ki te 2.

$$x=-30$$

Kua oti te whārite te whakatau.

$$x=36 x=-30$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,6 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 5x\left(x-6\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-6,x,5.

$$5x\times 36-\left(5x-30\right)\times 36=x\left(x-6\right)$$

Whakareatia te 5 ki te 36, ka 180.

$$180x-\left(5x-30\right)\times 36=x\left(x-6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5x-30 ki te 36.

$$180x-\left(180x-1080\right)=x\left(x-6\right)$$

Hei kimi i te tauaro o 180x-1080, kimihia te tauaro o ia taurangi.

$$180x-180x+1080=x\left(x-6\right)$$

Pahekotia te 180x me -180x, ka 0.

$$1080=x\left(x-6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-6.

$$1080=x^{2}-6x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-6x=1080$$

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.

$$x^{2}-6x+\left(-3\right)^{2}=1080+\left(-3\right)^{2}$$

Pūrua -3.

$$x^{2}-6x+9=1080+9$$

Tāpiri 1080 ki te 9.

$$x^{2}-6x+9=1089$$

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}.

$$\left(x-3\right)^{2}=1089$$

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

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{1089}$$

Whakarūnātia.

$$x-3=33 x-3=-33$$

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

$$x=36 x=-30$$