Whakaoti i te x+1/x-1=2x-5/2x-7

$$\frac { x + 1 } { x - 1 } = \frac { 2 x - 5 } { 2 x - 7 }$$

Whakaoti mō x

$$x=6$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 1,\frac{7}{2} 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(2x-7\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-1,2x-7.

$$\left(2x-7\right)\left(x+1\right)=\left(x-1\right)\left(2x-5\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-7 ki te x+1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x-7=\left(x-1\right)\left(2x-5\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te 2x-5 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x-7=2x^{2}-7x+5$$

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

$$2x^{2}-5x-7-2x^{2}=-7x+5$$

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

$$-5x-7=-7x+5$$

Me tāpiri te 7x ki ngā taha e rua.

$$-5x-7+7x=5$$

Pahekotia te -5x me 7x, ka 2x.

$$2x-7=5$$

Me tāpiri te 7 ki ngā taha e rua.

$$2x=5+7$$

Tāpirihia te 5 ki te 7, ka 12.

$$2x=12$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{12}{2}$$

Whakawehea te 12 ki te 2, kia riro ko 6.

$$x=6$$