Whakaoti i te a-1/a^2+a-1/2a-2-1/2a+2=1-2a/a(a^2-1)

$$\frac { a - 1 } { a ^ { 2 } + a } - \frac { 1 } { 2 a - 2 } - \frac { 1 } { 2 a + 2 } = \frac { 1 - 2 a } { a ( a ^ { 2 } - 1 ) }$$

Whakaoti mō a (complex solution)

$$a\in \mathrm{C}\setminus -1,0,1$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe a ki tētahi o ngā uara -1,0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2a\left(a-1\right)\left(a+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o a^{2}+a,2a-2,2a+2,a\left(a^{2}-1\right).

$$\left(2a-2\right)\left(a-1\right)-\left(a+1\right)a-\left(a-1\right)a=2\left(1-2a\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2a-2 ki te a-1 ka whakakotahi i ngā kupu rite.

$$2a^{2}-4a+2-\left(a+1\right)a-\left(a-1\right)a=2\left(1-2a\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+1 ki te a.

$$2a^{2}-4a+2-\left(a^{2}+a\right)-\left(a-1\right)a=2\left(1-2a\right)$$

Hei kimi i te tauaro o a^{2}+a, kimihia te tauaro o ia taurangi.

$$2a^{2}-4a+2-a^{2}-a-\left(a-1\right)a=2\left(1-2a\right)$$

Pahekotia te 2a^{2} me -a^{2}, ka a^{2}.

$$a^{2}-4a+2-a-\left(a-1\right)a=2\left(1-2a\right)$$

Pahekotia te -4a me -a, ka -5a.

$$a^{2}-5a+2-\left(a-1\right)a=2\left(1-2a\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te a-1 ki te a.

$$a^{2}-5a+2-\left(a^{2}-a\right)=2\left(1-2a\right)$$

Hei kimi i te tauaro o a^{2}-a, kimihia te tauaro o ia taurangi.

$$a^{2}-5a+2-a^{2}+a=2\left(1-2a\right)$$

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

$$-5a+2+a=2\left(1-2a\right)$$

Pahekotia te -5a me a, ka -4a.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 1-2a.

$$-4a+2=2-4a$$

Tangohia te 2 mai i ngā taha e rua.

$$-4a+2-2=-4a$$

Tangohia te 2 i te 2, ka 0.

$$-4a=-4a$$

Me tāpiri te 4a ki ngā taha e rua.

$$-4a+4a=0$$

Pahekotia te -4a me 4a, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi a ahakoa.

$$a\in \mathrm{C}$$

Tē taea kia ōrite te tāupe a ki tētahi o ngā uara -1,1,0.

$$a\in \mathrm{C}\setminus -1,0,1$$

Whakaoti mō a

$$a\in \mathrm{R}\setminus -1,0,1$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe a ki tētahi o ngā uara -1,0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2a\left(a-1\right)\left(a+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o a^{2}+a,2a-2,2a+2,a\left(a^{2}-1\right).

$$\left(2a-2\right)\left(a-1\right)-\left(a+1\right)a-\left(a-1\right)a=2\left(1-2a\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2a-2 ki te a-1 ka whakakotahi i ngā kupu rite.

$$2a^{2}-4a+2-\left(a+1\right)a-\left(a-1\right)a=2\left(1-2a\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+1 ki te a.

$$2a^{2}-4a+2-\left(a^{2}+a\right)-\left(a-1\right)a=2\left(1-2a\right)$$

Hei kimi i te tauaro o a^{2}+a, kimihia te tauaro o ia taurangi.

$$2a^{2}-4a+2-a^{2}-a-\left(a-1\right)a=2\left(1-2a\right)$$

Pahekotia te 2a^{2} me -a^{2}, ka a^{2}.

$$a^{2}-4a+2-a-\left(a-1\right)a=2\left(1-2a\right)$$

Pahekotia te -4a me -a, ka -5a.

$$a^{2}-5a+2-\left(a-1\right)a=2\left(1-2a\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te a-1 ki te a.

$$a^{2}-5a+2-\left(a^{2}-a\right)=2\left(1-2a\right)$$

Hei kimi i te tauaro o a^{2}-a, kimihia te tauaro o ia taurangi.

$$a^{2}-5a+2-a^{2}+a=2\left(1-2a\right)$$

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

$$-5a+2+a=2\left(1-2a\right)$$

Pahekotia te -5a me a, ka -4a.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 1-2a.

$$-4a+2=2-4a$$

Tangohia te 2 mai i ngā taha e rua.

$$-4a+2-2=-4a$$

Tangohia te 2 i te 2, ka 0.

$$-4a=-4a$$

Me tāpiri te 4a ki ngā taha e rua.

$$-4a+4a=0$$

Pahekotia te -4a me 4a, ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi a ahakoa.

$$a\in \mathrm{R}$$

Tē taea kia ōrite te tāupe a ki tētahi o ngā uara -1,1,0.

$$a\in \mathrm{R}\setminus -1,0,1$$