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

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

Whakaoti mō x

$$x=2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -3,1 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+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}+2x-3,x+3,x-1.

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

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

$$x-1+4x-4=x+3$$

Pahekotia te x me 4x, ka 5x.

$$5x-1-4=x+3$$

Tangohia te 4 i te -1, ka -5.

$$5x-5=x+3$$

Tangohia te x mai i ngā taha e rua.

$$5x-5-x=3$$

Pahekotia te 5x me -x, ka 4x.

$$4x-5=3$$

Me tāpiri te 5 ki ngā taha e rua.

$$4x=3+5$$

Tāpirihia te 3 ki te 5, ka 8.

$$4x=8$$

Whakawehea ngā taha e rua ki te 4.

$$x=\frac{8}{4}$$

Whakawehea te 8 ki te 4, kia riro ko 2.

$$x=2$$