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

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

Whakaoti mō x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+x-2 ki te -1.

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

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

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

Pahekotia te 2x me -x, ka x.

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

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

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

Tangohia te 3x mai i ngā taha e rua.

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

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

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

Tangohia te 2 mai i ngā taha e rua.

$$-2x=-3-2$$

Tangohia te 2 i te -3, ka -5.

$$-2x=-5$$

Whakawehea ngā taha e rua ki te -2.

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

Ka taea te hautanga \frac{-5}{-2} te whakamāmā ki te \frac{5}{2} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

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