Whakaoti i te x/2k^2-2+1-2x/k^2-k-2=1/k^2-3k+2

$$\frac { x } { 2 k ^ { 2 } - 2 } + \frac { 1 - 2 x } { k ^ { 2 } - k - 2 } = \frac { 1 } { k ^ { 2 } - 3 k + 2 }$$

Whakaoti mō k (complex solution)

$$k=\frac{2}{3}-\frac{4}{3x}$$

$$x\neq \frac{4}{5}\text{ and }x\neq 0\text{ and }x\neq -4\text{ and }x\neq -1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te k-2 ki te x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2k-2 ki te 1-2x.

$$kx-2x+2k-4xk-2+4x=2k+2$$

Pahekotia te kx me -4xk, ka -3kx.

$$-3kx-2x+2k-2+4x=2k+2$$

Pahekotia te -2x me 4x, ka 2x.

$$-3kx+2x+2k-2=2k+2$$

Tangohia te 2k mai i ngā taha e rua.

$$-3kx+2x+2k-2-2k=2$$

Pahekotia te 2k me -2k, ka 0.

$$-3kx+2x-2=2$$

Tangohia te 2x mai i ngā taha e rua.

$$-3kx-2=2-2x$$

Me tāpiri te 2 ki ngā taha e rua.

$$-3kx=2-2x+2$$

Tāpirihia te 2 ki te 2, ka 4.

$$-3kx=4-2x$$

He hanga arowhānui tō te whārite.

$$\left(-3x\right)k=4-2x$$

Whakawehea ngā taha e rua ki te -3x.

$$\frac{\left(-3x\right)k}{-3x}=\frac{4-2x}{-3x}$$

Mā te whakawehe ki te -3x ka wetekia te whakareanga ki te -3x.

$$k=\frac{4-2x}{-3x}$$

Whakawehe 4-2x ki te -3x.

$$k=\frac{2}{3}-\frac{4}{3x}$$

Tē taea kia ōrite te tāupe k ki tētahi o ngā uara -1,1,2.

$$k=\frac{2}{3}-\frac{4}{3x}\text{, }k\neq -1\text{ and }k\neq 1\text{ and }k\neq 2$$

Whakaoti mō x (complex solution)

$$x=\frac{4}{2-3k}$$

$$k\neq \frac{2}{3}\text{ and }k\neq -1\text{ and }k\neq 1\text{ and }k\neq 2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 2\left(k-2\right)\left(k-1\right)\left(k+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2k^{2}-2,k^{2}-k-2,k^{2}-3k+2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te k-2 ki te x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2k-2 ki te 1-2x.

$$kx-2x+2k-4kx-2+4x=2k+2$$

Pahekotia te kx me -4kx, ka -3kx.

$$-3kx-2x+2k-2+4x=2k+2$$

Pahekotia te -2x me 4x, ka 2x.

$$-3kx+2x+2k-2=2k+2$$

Tangohia te 2k mai i ngā taha e rua.

$$-3kx+2x-2=2k+2-2k$$

Pahekotia te 2k me -2k, ka 0.

$$-3kx+2x-2=2$$

Me tāpiri te 2 ki ngā taha e rua.

$$-3kx+2x=2+2$$

Tāpirihia te 2 ki te 2, ka 4.

$$-3kx+2x=4$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-3k+2\right)x=4$$

He hanga arowhānui tō te whārite.

$$\left(2-3k\right)x=4$$

Whakawehea ngā taha e rua ki te 2-3k.

$$\frac{\left(2-3k\right)x}{2-3k}=\frac{4}{2-3k}$$

Mā te whakawehe ki te 2-3k ka wetekia te whakareanga ki te 2-3k.

$$x=\frac{4}{2-3k}$$

Whakaoti mō k

$$k=\frac{2}{3}-\frac{4}{3x}$$

$$x\neq -4\text{ and }x\neq 0\text{ and }x\neq \frac{4}{5}\text{ and }x\neq -1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te k-2 ki te x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2k-2 ki te 1-2x.

$$kx-2x+2k-4xk-2+4x=2k+2$$

Pahekotia te kx me -4xk, ka -3kx.

$$-3kx-2x+2k-2+4x=2k+2$$

Pahekotia te -2x me 4x, ka 2x.

$$-3kx+2x+2k-2=2k+2$$

Tangohia te 2k mai i ngā taha e rua.

$$-3kx+2x+2k-2-2k=2$$

Pahekotia te 2k me -2k, ka 0.

$$-3kx+2x-2=2$$

Tangohia te 2x mai i ngā taha e rua.

$$-3kx-2=2-2x$$

Me tāpiri te 2 ki ngā taha e rua.

$$-3kx=2-2x+2$$

Tāpirihia te 2 ki te 2, ka 4.

$$-3kx=4-2x$$

He hanga arowhānui tō te whārite.

$$\left(-3x\right)k=4-2x$$

Whakawehea ngā taha e rua ki te -3x.

$$\frac{\left(-3x\right)k}{-3x}=\frac{4-2x}{-3x}$$

Mā te whakawehe ki te -3x ka wetekia te whakareanga ki te -3x.

$$k=\frac{4-2x}{-3x}$$

Whakawehe 4-2x ki te -3x.

$$k=\frac{2}{3}-\frac{4}{3x}$$

Tē taea kia ōrite te tāupe k ki tētahi o ngā uara -1,1,2.

$$k=\frac{2}{3}-\frac{4}{3x}\text{, }k\neq -1\text{ and }k\neq 1\text{ and }k\neq 2$$

Whakaoti mō x

$$x=\frac{4}{2-3k}$$

$$k\neq \frac{2}{3}\text{ and }k\neq 2\text{ and }|k|\neq 1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 2\left(k-2\right)\left(k-1\right)\left(k+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2k^{2}-2,k^{2}-k-2,k^{2}-3k+2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te k-2 ki te x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2k-2 ki te 1-2x.

$$kx-2x+2k-4kx-2+4x=2k+2$$

Pahekotia te kx me -4kx, ka -3kx.

$$-3kx-2x+2k-2+4x=2k+2$$

Pahekotia te -2x me 4x, ka 2x.

$$-3kx+2x+2k-2=2k+2$$

Tangohia te 2k mai i ngā taha e rua.

$$-3kx+2x-2=2k+2-2k$$

Pahekotia te 2k me -2k, ka 0.

$$-3kx+2x-2=2$$

Me tāpiri te 2 ki ngā taha e rua.

$$-3kx+2x=2+2$$

Tāpirihia te 2 ki te 2, ka 4.

$$-3kx+2x=4$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-3k+2\right)x=4$$

He hanga arowhānui tō te whārite.

$$\left(2-3k\right)x=4$$

Whakawehea ngā taha e rua ki te 2-3k.

$$\frac{\left(2-3k\right)x}{2-3k}=\frac{4}{2-3k}$$

Mā te whakawehe ki te 2-3k ka wetekia te whakareanga ki te 2-3k.

$$x=\frac{4}{2-3k}$$