Whakaoti i te x+1/3-x+1/x+2=0

$$\frac { x + 1 } { 3 } - \frac { x + 1 } { x + 2 } = 0$$

Whakaoti mō x

$$x=1$$

$$x=-1$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tē taea kia ōrite te tāupe x ki -2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o 3,x+2.

$$\left(x+2\right)\left(x+1\right)-3\left(x+1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}+3x+2-3\left(x+1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te x+1.

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

Pahekotia te 3x me -3x, ka 0.

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

Tangohia te 3 i te 2, ka -1.

$$x^{2}-1=0$$

Whakaarohia te x^{2}-1. Tuhia anō te x^{2}-1 hei x^{2}-1^{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).

$$\left(x-1\right)\left(x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+1=0.

$$x=1 x=-1$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki -2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o 3,x+2.

$$\left(x+2\right)\left(x+1\right)-3\left(x+1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}+3x+2-3\left(x+1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te x+1.

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

Pahekotia te 3x me -3x, ka 0.

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

Tangohia te 3 i te 2, ka -1.

$$x^{2}-1=0$$

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}=1$$

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

$$x=1 x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o 3,x+2.

$$\left(x+2\right)\left(x+1\right)-3\left(x+1\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}+3x+2-3\left(x+1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te x+1.

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

Pahekotia te 3x me -3x, ka 0.

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

Tangohia te 3 i te 2, ka -1.

$$x^{2}-1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)}}{2}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{0±2}{2}$$

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

$$x=1$$

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

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=1 x=-1$$