Whakaoti i te x^2/(2-x)(10-x)=1

$$\frac { x ^ { 2 } } { ( 2 - x ) ( 10 - x ) } = 1$$

Whakaoti mō x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 2,10 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(x-10\right)\left(x-2\right).

$$x^{2}=\left(x-10\right)\left(x-2\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-10 ki te x-2 ka whakakotahi i ngā kupu rite.

$$x^{2}=x^{2}-12x+20$$

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

$$x^{2}-x^{2}=-12x+20$$

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

$$0=-12x+20$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-12x+20=0$$

Tangohia te 20 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-12x=-20$$

Whakawehea ngā taha e rua ki te -12.

$$x=\frac{-20}{-12}$$

Whakahekea te hautanga \frac{-20}{-12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -4.

$$x=\frac{5}{3}$$