Whakaoti i te 3/x+1=x/x-1-1

$$\frac{ 3 }{ x+1 } = \frac{ x }{ x-1 } -1$$

Whakaoti mō x

$$x=2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\left(x-1\right)\times 3=\left(x+1\right)x+\left(x-1\right)\left(x+1\right)\left(-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-1 ki te 3.

$$3x-3=\left(x+1\right)x+\left(x-1\right)\left(x+1\right)\left(-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+1 ki te x.

$$3x-3=x^{2}+x+\left(x-1\right)\left(x+1\right)\left(-1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x+1 ka whakakotahi i ngā kupu rite.

$$3x-3=x^{2}+x+\left(x^{2}-1\right)\left(-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}-1 ki te -1.

$$3x-3=x^{2}+x-x^{2}+1$$

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

$$3x-3=x+1$$

Tangohia te x mai i ngā taha e rua.

$$3x-3-x=1$$

Pahekotia te 3x me -x, ka 2x.

$$2x-3=1$$

Me tāpiri te 3 ki ngā taha e rua.

$$2x=1+3$$

Tāpirihia te 1 ki te 3, ka 4.

$$2x=4$$

Whakawehea ngā taha e rua ki te 2.

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

Whakawehea te 4 ki te 2, kia riro ko 2.

$$x=2$$