Whakaoti i te 2/x+2+5/x-2=6/x^2-4

$$\frac { 2 } { x + 2 } + \frac { 5 } { x - 2 } = \frac { 6 } { x ^ { 2 } - 4 }$$

Whakaoti mō x

$$x=0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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,x-2,x^{2}-4.

$$\left(x-2\right)\times 2+\left(x+2\right)\times 5=6$$

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

$$2x-4+\left(x+2\right)\times 5=6$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te 5.

$$2x-4+5x+10=6$$

Pahekotia te 2x me 5x, ka 7x.

$$7x-4+10=6$$

Tāpirihia te -4 ki te 10, ka 6.

$$7x+6=6$$

Tangohia te 6 mai i ngā taha e rua.

$$7x=6-6$$

Tangohia te 6 i te 6, ka 0.

$$7x=0$$

He ōrite te hua o ngā tau e rua ki 0 ina 0 tētahi o rāua te iti rawa. Tātemea kāore te 7 e ōrite ki 0, me ōrite pū te x ki 0.

$$x=0$$