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

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

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,x-1.

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

Whakaarohia te \left(x-1\right)\left(x+1\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 1.

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

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

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

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

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

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

$$-1=-2x$$

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

$$-2x=-1$$

Whakawehea ngā taha e rua ki te -2.

$$x=\frac{-1}{-2}$$

Ka taea te hautanga \frac{-1}{-2} te whakamāmā ki te \frac{1}{2} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{1}{2}$$