Whakaoti i te 1/2x-1-1/2x+1=1/4=

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

Whakaoti mō x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{1}{2},\frac{1}{2} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4\left(2x-1\right)\left(2x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x-1,2x+1,4.

$$8x+4-\left(8x-4\right)=\left(2x-1\right)\left(2x+1\right)$$

Hei kimi i te tauaro o 8x-4, kimihia te tauaro o ia taurangi.

$$8x+4-8x+4=\left(2x-1\right)\left(2x+1\right)$$

Pahekotia te 8x me -8x, ka 0.

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

Tāpirihia te 4 ki te 4, ka 8.

$$8=\left(2x-1\right)\left(2x+1\right)$$

Whakaarohia te \left(2x-1\right)\left(2x+1\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 1.

$$8=\left(2x\right)^{2}-1$$

Whakarohaina te \left(2x\right)^{2}.

$$8=2^{2}x^{2}-1$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$8=4x^{2}-1$$

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

$$4x^{2}-1=8$$

Me tāpiri te 1 ki ngā taha e rua.

$$4x^{2}=8+1$$

Tāpirihia te 8 ki te 1, ka 9.

$$4x^{2}=9$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{9}{4}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{1}{2},\frac{1}{2} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4\left(2x-1\right)\left(2x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x-1,2x+1,4.

$$8x+4-\left(8x-4\right)=\left(2x-1\right)\left(2x+1\right)$$

Hei kimi i te tauaro o 8x-4, kimihia te tauaro o ia taurangi.

$$8x+4-8x+4=\left(2x-1\right)\left(2x+1\right)$$

Pahekotia te 8x me -8x, ka 0.

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

Tāpirihia te 4 ki te 4, ka 8.

$$8=\left(2x-1\right)\left(2x+1\right)$$

Whakaarohia te \left(2x-1\right)\left(2x+1\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 1.

$$8=\left(2x\right)^{2}-1$$

Whakarohaina te \left(2x\right)^{2}.

$$8=2^{2}x^{2}-1$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$8=4x^{2}-1$$

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

$$4x^{2}-1=8$$

Tangohia te 8 mai i ngā taha e rua.

$$4x^{2}-1-8=0$$

Tangohia te 8 i te -1, ka -9.

$$4x^{2}-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-9\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-9\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-9\right)}}{2\times 4}$$

Whakareatia -16 ki te -9.

$$x=\frac{0±\sqrt{144}}{2\times 4}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{0±12}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±12}{8}$$

Nā, me whakaoti te whārite x=\frac{0±12}{8} ina he tāpiri te ±. Whakahekea te hautanga \frac{12}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{3}{2}$$

Nā, me whakaoti te whārite x=\frac{0±12}{8} ina he tango te ±. Whakahekea te hautanga \frac{-12}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Kua oti te whārite te whakatau.

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