Whakaoti i te x^2-8/x+4=8/x+4

$$\frac { x ^ { 2 } - 8 } { x + 4 } = \frac { 8 } { x + 4 }$$

Whakaoti mō x

$$x=4$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tē taea kia ōrite te tāupe x ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+4.

$$x^{2}-8=8$$

Tangohia te 8 mai i ngā taha e rua.

$$x^{2}-8-8=0$$

Tangohia te 8 i te -8, ka -16.

$$x^{2}-16=0$$

Whakaarohia te x^{2}-16. Tuhia anō te x^{2}-16 hei x^{2}-4^{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).

$$\left(x-4\right)\left(x+4\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-4=0 me te x+4=0.

$$x=4 x=-4$$

Tē taea kia ōrite te tāupe x ki -4.

$$x=4$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+4.

$$x^{2}-8=8$$

Me tāpiri te 8 ki ngā taha e rua.

$$x^{2}=8+8$$

Tāpirihia te 8 ki te 8, ka 16.

$$x^{2}=16$$

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

$$x=4 x=-4$$

Tē taea kia ōrite te tāupe x ki -4.

$$x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+4.

$$x^{2}-8=8$$

Tangohia te 8 mai i ngā taha e rua.

$$x^{2}-8-8=0$$

Tangohia te 8 i te -8, ka -16.

$$x^{2}-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Whakareatia -4 ki te -16.

$$x=\frac{0±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{0±8}{2}$$

Nā, me whakaoti te whārite x=\frac{0±8}{2} ina he tāpiri te ±. Whakawehe 8 ki te 2.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{0±8}{2} ina he tango te ±. Whakawehe -8 ki te 2.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=4 x=-4$$

Tē taea kia ōrite te tāupe x ki -4.

$$x=4$$