Whakaoti i te x-2/x-5=x/x-1

$$\frac{ x-2 }{ x-5 } = \frac{ x }{ x-1 }$$

Whakaoti mō x

$$x=-1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 1,5 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-5,x-1.

$$\left(x-1\right)\left(x-2\right)=\left(x-5\right)x$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x-2 ka whakakotahi i ngā kupu rite.

$$x^{2}-3x+2=\left(x-5\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-5 ki te x.

$$x^{2}-3x+2=x^{2}-5x$$

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

$$x^{2}-3x+2-x^{2}=-5x$$

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

$$-3x+2=-5x$$

Me tāpiri te 5x ki ngā taha e rua.

$$-3x+2+5x=0$$

Pahekotia te -3x me 5x, ka 2x.

$$2x+2=0$$

Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2x=-2$$

Whakawehea ngā taha e rua ki te 2.

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

Whakawehea te -2 ki te 2, kia riro ko -1.

$$x=-1$$