Whakaoti i te x/x-1+2x/x+1=3

$$\frac { x } { x - 1 } + \frac { 2 x } { x + 1 } = 3$$

Whakaoti mō x

$$x=3$$

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.

$$\left(x+1\right)x+\left(x-1\right)\times 2x=3\left(x-1\right)\left(x+1\right)$$

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

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

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

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

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

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

Pahekotia te x^{2} me 2x^{2}, ka 3x^{2}.

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

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

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

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

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-3 ki te x+1 ka whakakotahi i ngā kupu rite.

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

Tangohia te 3x^{2} mai i ngā taha e rua.

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

Pahekotia te 3x^{2} me -3x^{2}, ka 0.

$$-x=-3$$

Me whakarea ngā taha e rua ki te -1.

$$x=3$$