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

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

Whakaoti mō x

$$x=8$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

$$x^{2}-2x=\left(x-4\right)\left(x+4\right)$$

Whakaarohia te \left(x-4\right)\left(x+4\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 4.

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

Tangohia te x^{2} mai i ngā taha e rua.

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

Pahekotia te x^{2} me -x^{2}, ka 0.

$$-2x=-16$$

Whakawehea ngā taha e rua ki te -2.

$$x=\frac{-16}{-2}$$

Whakawehea te -16 ki te -2, kia riro ko 8.

$$x=8$$