Whakaoti i te x+6/x^2-4+1/x+2=2/x-2

$$\frac{ x+6 }{ { x }^{ 2 } -4 } + \frac{ 1 }{ x+2 } = \frac{ 2 }{ x-2 }$$

Whakaoti mō x (complex solution)

$$x\in \mathrm{C}\setminus -2,2$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-4,x+2,x-2.

$$x+6+x-2=\left(x+2\right)\times 2$$

Pahekotia te x me x, ka 2x.

$$2x+6-2=\left(x+2\right)\times 2$$

Tangohia te 2 i te 6, ka 4.

$$2x+4=\left(x+2\right)\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te 2.

$$2x+4=2x+4$$

Tangohia te 2x mai i ngā taha e rua.

$$2x+4-2x=4$$

Pahekotia te 2x me -2x, ka 0.

$$4=4$$

Whakatauritea te 4 me te 4.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

$$x\in \mathrm{C}$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,2.

$$x\in \mathrm{C}\setminus -2,2$$

Whakaoti mō x

$$x\in \mathrm{R}\setminus 2,-2$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-4,x+2,x-2.

$$x+6+x-2=\left(x+2\right)\times 2$$

Pahekotia te x me x, ka 2x.

$$2x+6-2=\left(x+2\right)\times 2$$

Tangohia te 2 i te 6, ka 4.

$$2x+4=\left(x+2\right)\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te 2.

$$2x+4=2x+4$$

Tangohia te 2x mai i ngā taha e rua.

$$2x+4-2x=4$$

Pahekotia te 2x me -2x, ka 0.

$$4=4$$

Whakatauritea te 4 me te 4.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

$$x\in \mathrm{R}$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,2.

$$x\in \mathrm{R}\setminus -2,2$$