Whakaoti i te (k-1)(k+1)x=2(k-1)(k+2)

$$( k - 1 ) ( k + 1 ) x = 2 ( k - 1 ) ( k + 2 )$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{2\left(k+2\right)}{k+1}\text{, }&k\neq -1\\x\in \mathrm{R}\text{, }&k=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

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

$$k^{2}x-x=\left(2k-2\right)\left(k+2\right)$$

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

$$k^{2}x-x=2k^{2}+2k-4$$

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

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

Whakawehea ngā taha e rua ki te k^{2}-1.

$$\frac{\left(k^{2}-1\right)x}{k^{2}-1}=\frac{2\left(k-1\right)\left(k+2\right)}{k^{2}-1}$$

Mā te whakawehe ki te k^{2}-1 ka wetekia te whakareanga ki te k^{2}-1.

$$x=\frac{2\left(k-1\right)\left(k+2\right)}{k^{2}-1}$$

Whakawehe 2\left(-1+k\right)\left(2+k\right) ki te k^{2}-1.

$$x=\frac{2\left(k+2\right)}{k+1}$$

Whakaoti mō k

$$\left\{\begin{matrix}\\k=1\text{, }&\text{unconditionally}\\k=-\frac{x-4}{x-2}\text{, }&x\neq 2\end{matrix}\right.$$