Whakaoti i te 4/x-1+2/x+1=3/x^2-1

$$\frac { 4 } { x - 1 } + \frac { 2 } { x + 1 } = \frac { 3 } { x ^ { 2 } - 1 }$$

Whakaoti mō x

$$x=\frac{1}{6}\approx 0.166666667$$

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,x^{2}-1.

$$\left(x+1\right)\times 4+\left(x-1\right)\times 2=3$$

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

$$4x+4+\left(x-1\right)\times 2=3$$

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

$$4x+4+2x-2=3$$

Pahekotia te 4x me 2x, ka 6x.

$$6x+4-2=3$$

Tangohia te 2 i te 4, ka 2.

$$6x+2=3$$

Tangohia te 2 mai i ngā taha e rua.

$$6x=3-2$$

Tangohia te 2 i te 3, ka 1.

$$6x=1$$

Whakawehea ngā taha e rua ki te 6.

$$x=\frac{1}{6}$$