Whakaoti i te 2/3-6x^2/9x^2-1=2/3x-1

$$\frac { 2 } { 3 } - \frac { 6 x ^ { 2 } } { 9 x ^ { 2 } - 1 } = \frac { 2 } { 3 x - 1 }$$

Whakaoti mō x

$$x=-\frac{4}{9}\approx -0.444444444$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{1}{3},\frac{1}{3} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(3x-1\right)\left(3x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 3,9x^{2}-1,3x-1.

$$3\left(3x-1\right)\left(3x+1\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

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

$$\left(9x-3\right)\left(3x+1\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 9x-3 ki te 3x+1 ka whakakotahi i ngā kupu rite.

$$\left(27x^{2}-3\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te 27x^{2}-3 ki te \frac{2}{3}.

$$18x^{2}-2-3\times 6x^{2}=\left(9x+3\right)\times 2$$

Whakareatia te -3 ki te 6, ka -18.

$$18x^{2}-2-18x^{2}=\left(9x+3\right)\times 2$$

Pahekotia te 18x^{2} me -18x^{2}, ka 0.

$$-2=\left(9x+3\right)\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9x+3 ki te 2.

$$-2=18x+6$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$18x+6=-2$$

Tangohia te 6 mai i ngā taha e rua.

$$18x=-2-6$$

Tangohia te 6 i te -2, ka -8.

$$18x=-8$$

Whakawehea ngā taha e rua ki te 18.

$$x=\frac{-8}{18}$$

Whakahekea te hautanga \frac{-8}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{4}{9}$$