Whakaoti i te 5/x^2-x-6=3/x^2-4+3/2x^2-10x+12

$$\frac{ 5 }{ { x }^{ 2 } -x-6 } = \frac{ 3 }{ { x }^{ 2 } -4 } + \frac{ 3 }{ 2 { x }^{ 2 } -10x+12 }$$

Whakaoti mō x

$$x=8$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,2,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2\left(x-3\right)\left(x-2\right)\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}-x-6,x^{2}-4,2x^{2}-10x+12.

$$\left(2x-4\right)\times 5=\left(2x-6\right)\times 3+\left(x+2\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x-4 ki te 5.

$$10x-20=\left(2x-6\right)\times 3+\left(x+2\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x-6 ki te 3.

$$10x-20=6x-18+\left(x+2\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te 3.

$$10x-20=6x-18+3x+6$$

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

$$10x-20=9x-18+6$$

Tāpirihia te -18 ki te 6, ka -12.

$$10x-20=9x-12$$

Tangohia te 9x mai i ngā taha e rua.

$$10x-20-9x=-12$$

Pahekotia te 10x me -9x, ka x.

$$x-20=-12$$

Me tāpiri te 20 ki ngā taha e rua.

$$x=-12+20$$

Tāpirihia te -12 ki te 20, ka 8.

$$x=8$$