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

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

Whakaoti mō x

$$x=11$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\left(x-3\right)\left(x-3\right)+\left(x+2\right)\left(x-2\right)=2x^{2}-5x-6$$

Whakareatia te x-3 ki te x-3, ka \left(x-3\right)^{2}.

$$\left(x-3\right)^{2}+\left(x+2\right)\left(x-2\right)=2x^{2}-5x-6$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-3\right)^{2}.

$$x^{2}-6x+9+\left(x+2\right)\left(x-2\right)=2x^{2}-5x-6$$

Whakaarohia te \left(x+2\right)\left(x-2\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 2.

$$x^{2}-6x+9+x^{2}-4=2x^{2}-5x-6$$

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

$$2x^{2}-6x+9-4=2x^{2}-5x-6$$

Tangohia te 4 i te 9, ka 5.

$$2x^{2}-6x+5=2x^{2}-5x-6$$

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

$$2x^{2}-6x+5-2x^{2}=-5x-6$$

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

$$-6x+5=-5x-6$$

Me tāpiri te 5x ki ngā taha e rua.

$$-6x+5+5x=-6$$

Pahekotia te -6x me 5x, ka -x.

$$-x+5=-6$$

Tangohia te 5 mai i ngā taha e rua.

$$-x=-6-5$$

Tangohia te 5 i te -6, ka -11.

$$-x=-11$$

Me whakarea ngā taha e rua ki te -1.

$$x=11$$