Whakaoti i te 3x+4/x^2+x-2=4/x-1+5/x+2

$$\frac { 3 x + 4 } { x ^ { 2 } + x - 2 } = \frac { 4 } { x - 1 } + \frac { 5 } { x + 2 }$$

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 -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^{2}+x-2,x-1,x+2.

$$3x+4=\left(x+2\right)\times 4+\left(x-1\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te 4.

$$3x+4=4x+8+\left(x-1\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-1 ki te 5.

$$3x+4=4x+8+5x-5$$

Pahekotia te 4x me 5x, ka 9x.

$$3x+4=9x+8-5$$

Tangohia te 5 i te 8, ka 3.

$$3x+4=9x+3$$

Tangohia te 9x mai i ngā taha e rua.

$$3x+4-9x=3$$

Pahekotia te 3x me -9x, ka -6x.

$$-6x+4=3$$

Tangohia te 4 mai i ngā taha e rua.

$$-6x=3-4$$

Tangohia te 4 i te 3, ka -1.

$$-6x=-1$$

Whakawehea ngā taha e rua ki te -6.

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

Ka taea te hautanga \frac{-1}{-6} te whakamāmā ki te \frac{1}{6} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

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