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

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

Whakaoti mō x

$$x=\frac{1}{4}=0.25$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{1}{2},0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4x\left(2x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 4x,2x+1.

$$\left(2x+1\right)\left(2x-1\right)=4x\left(x-1\right)$$

Whakaarohia te \left(2x+1\right)\left(2x-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.

$$\left(2x\right)^{2}-1=4x\left(x-1\right)$$

Whakarohaina te \left(2x\right)^{2}.

$$2^{2}x^{2}-1=4x\left(x-1\right)$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$4x^{2}-1=4x\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x-1.

$$4x^{2}-1=4x^{2}-4x$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$4x^{2}-1-4x^{2}=-4x$$

Pahekotia te 4x^{2} me -4x^{2}, ka 0.

$$-1=-4x$$

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

$$-4x=-1$$

Whakawehea ngā taha e rua ki te -4.

$$x=\frac{-1}{-4}$$

Ka taea te hautanga \frac{-1}{-4} te whakamāmā ki te \frac{1}{4} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{1}{4}$$