Whakaoti i te 9/x-3-27/x(x-3)=-3

$$\frac { 9 } { x - 3 } - \frac { 27 } { x ( x - 3 ) } = - 3$$

Whakaoti mō x

$$x=-3$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-3,x\left(x-3\right).

$$x\times 9-27=-3x\left(x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3x ki te x-3.

$$x\times 9-27=-3x^{2}+9x$$

Me tāpiri te 3x^{2} ki ngā taha e rua.

$$x\times 9-27+3x^{2}=9x$$

Tangohia te 9x mai i ngā taha e rua.

$$x\times 9-27+3x^{2}-9x=0$$

Pahekotia te x\times 9 me -9x, ka 0.

$$-27+3x^{2}=0$$

Whakawehea ngā taha e rua ki te 3.

$$-9+x^{2}=0$$

Whakaarohia te -9+x^{2}. Tuhia anō te -9+x^{2} hei x^{2}-3^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-3=0 me te x+3=0.

$$x=3 x=-3$$

Tē taea kia ōrite te tāupe x ki 3.

$$x=-3$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-3,x\left(x-3\right).

$$x\times 9-27=-3x\left(x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3x ki te x-3.

$$x\times 9-27=-3x^{2}+9x$$

Me tāpiri te 3x^{2} ki ngā taha e rua.

$$x\times 9-27+3x^{2}=9x$$

Tangohia te 9x mai i ngā taha e rua.

$$x\times 9-27+3x^{2}-9x=0$$

Pahekotia te x\times 9 me -9x, ka 0.

$$-27+3x^{2}=0$$

Me tāpiri te 27 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$3x^{2}=27$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{27}{3}$$

Whakawehea te 27 ki te 3, kia riro ko 9.

$$x^{2}=9$$

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

$$x=3 x=-3$$

Tē taea kia ōrite te tāupe x ki 3.

$$x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-3,x\left(x-3\right).

$$x\times 9-27=-3x\left(x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3x ki te x-3.

$$x\times 9-27=-3x^{2}+9x$$

Me tāpiri te 3x^{2} ki ngā taha e rua.

$$x\times 9-27+3x^{2}=9x$$

Tangohia te 9x mai i ngā taha e rua.

$$x\times 9-27+3x^{2}-9x=0$$

Pahekotia te x\times 9 me -9x, ka 0.

$$-27+3x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$3x^{2}-27=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -27 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-27\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-27\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-27\right)}}{2\times 3}$$

Whakareatia -12 ki te -27.

$$x=\frac{0±\sqrt{324}}{2\times 3}$$

Tuhia te pūtakerua o te 324.

$$x=\frac{0±18}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±18}{6}$$

Nā, me whakaoti te whārite x=\frac{0±18}{6} ina he tāpiri te ±. Whakawehe 18 ki te 6.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{0±18}{6} ina he tango te ±. Whakawehe -18 ki te 6.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=3 x=-3$$

Tē taea kia ōrite te tāupe x ki 3.

$$x=-3$$