Whakaoti i te 3-x/x-2=x/x+2-2

$$\frac{ 3-x }{ x-2 } = \frac{ x }{ x+2 } -2$$

Whakaoti mō x

$$x=\frac{2}{3}\approx 0.666666667$$

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.

$$\left(x+2\right)\left(3-x\right)=\left(x-2\right)x+\left(x-2\right)\left(x+2\right)\left(-2\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te 3-x ka whakakotahi i ngā kupu rite.

$$x-x^{2}+6=\left(x-2\right)x+\left(x-2\right)\left(x+2\right)\left(-2\right)$$

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

$$x-x^{2}+6=x^{2}-2x+\left(x-2\right)\left(x+2\right)\left(-2\right)$$

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

$$x-x^{2}+6=x^{2}-2x+\left(x^{2}-4\right)\left(-2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}-4 ki te -2.

$$x-x^{2}+6=x^{2}-2x-2x^{2}+8$$

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

$$x-x^{2}+6=-x^{2}-2x+8$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$x-x^{2}+6+x^{2}=-2x+8$$

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

$$x+6=-2x+8$$

Me tāpiri te 2x ki ngā taha e rua.

$$x+6+2x=8$$

Pahekotia te x me 2x, ka 3x.

$$3x+6=8$$

Tangohia te 6 mai i ngā taha e rua.

$$3x=8-6$$

Tangohia te 6 i te 8, ka 2.

$$3x=2$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{2}{3}$$