Whakaoti i te x+3/x+9+7/x-9=7/x-9

$$\frac { x + 3 } { x + 9 } + \frac { 7 } { x - 9 } = \frac { 7 } { x - 9 }$$

Whakaoti mō x

$$x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -9,9 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-9\right)\left(x+9\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+9,x-9.

$$\left(x-9\right)\left(x+3\right)+\left(x+9\right)\times 7=\left(x+9\right)\times 7$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-9 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x^{2}-6x-27+\left(x+9\right)\times 7=\left(x+9\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+9 ki te 7.

$$x^{2}-6x-27+7x+63=\left(x+9\right)\times 7$$

Pahekotia te -6x me 7x, ka x.

$$x^{2}+x-27+63=\left(x+9\right)\times 7$$

Tāpirihia te -27 ki te 63, ka 36.

$$x^{2}+x+36=\left(x+9\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+9 ki te 7.

$$x^{2}+x+36=7x+63$$

Tangohia te 7x mai i ngā taha e rua.

$$x^{2}+x+36-7x=63$$

Pahekotia te x me -7x, ka -6x.

$$x^{2}-6x+36=63$$

Tangohia te 63 mai i ngā taha e rua.

$$x^{2}-6x+36-63=0$$

Tangohia te 63 i te 36, ka -27.

$$x^{2}-6x-27=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -6 mō b, me -27 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-27\right)}}{2}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-27\right)}}{2}$$

Whakareatia -4 ki te -27.

$$x=\frac{-\left(-6\right)±\sqrt{36+108}}{2}$$

Tāpiri 36 ki te 108.

$$x=\frac{-\left(-6\right)±\sqrt{144}}{2}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{-\left(-6\right)±12}{2}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±12}{2}$$

Nā, me whakaoti te whārite x=\frac{6±12}{2} ina he tāpiri te ±. Tāpiri 6 ki te 12.

$$x=\frac{18}{2}$$

Whakawehe 18 ki te 2.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{6±12}{2} ina he tango te ±. Tango 12 mai i 6.

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

Whakawehe -6 ki te 2.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=9 x=-3$$

Tē taea kia ōrite te tāupe x ki 9.

$$x=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -9,9 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-9\right)\left(x+9\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+9,x-9.

$$\left(x-9\right)\left(x+3\right)+\left(x+9\right)\times 7=\left(x+9\right)\times 7$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-9 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x^{2}-6x-27+\left(x+9\right)\times 7=\left(x+9\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+9 ki te 7.

$$x^{2}-6x-27+7x+63=\left(x+9\right)\times 7$$

Pahekotia te -6x me 7x, ka x.

$$x^{2}+x-27+63=\left(x+9\right)\times 7$$

Tāpirihia te -27 ki te 63, ka 36.

$$x^{2}+x+36=\left(x+9\right)\times 7$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+9 ki te 7.

$$x^{2}+x+36=7x+63$$

Tangohia te 7x mai i ngā taha e rua.

$$x^{2}+x+36-7x=63$$

Pahekotia te x me -7x, ka -6x.

$$x^{2}-6x+36=63$$

Tangohia te 36 mai i ngā taha e rua.

$$x^{2}-6x=63-36$$

Tangohia te 36 i te 63, ka 27.

$$x^{2}-6x=27$$

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.

$$x^{2}-6x+\left(-3\right)^{2}=27+\left(-3\right)^{2}$$

Pūrua -3.

$$x^{2}-6x+9=27+9$$

Tāpiri 27 ki te 9.

$$x^{2}-6x+9=36$$

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}.

$$\left(x-3\right)^{2}=36$$

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

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{36}$$

Whakarūnātia.

$$x-3=6 x-3=-6$$

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

$$x=9 x=-3$$

Tē taea kia ōrite te tāupe x ki 9.

$$x=-3$$