Whakaoti i te mx^2+(1-2m)x+1-3m=0

$$m x ^ { 2 } + ( 1 - 2 m ) x + 1 - 3 m = 0$$

Whakaoti mō m (complex solution)

$$\left\{\begin{matrix}m=-\frac{1}{x-3}\text{, }&x\neq 3\\m\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$mx^{2}+x-2mx+1-3m=0$$

Tangohia te x mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$mx^{2}-2mx+1-3m=-x$$

Tangohia te 1 mai i ngā taha e rua.

$$mx^{2}-2mx-3m=-x-1$$

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

$$\left(x^{2}-2x-3\right)m=-x-1$$

Whakawehea ngā taha e rua ki te x^{2}-2x-3.

$$\frac{\left(x^{2}-2x-3\right)m}{x^{2}-2x-3}=\frac{-x-1}{x^{2}-2x-3}$$

Mā te whakawehe ki te x^{2}-2x-3 ka wetekia te whakareanga ki te x^{2}-2x-3.

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

Whakawehe -x-1 ki te x^{2}-2x-3.

$$m=-\frac{1}{x-3}$$

Whakaoti mō m

$$\left\{\begin{matrix}m=-\frac{1}{x-3}\text{, }&x\neq 3\\m\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$mx^{2}+x-2mx+1-3m=0$$

Tangohia te x mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$mx^{2}-2mx+1-3m=-x$$

Tangohia te 1 mai i ngā taha e rua.

$$mx^{2}-2mx-3m=-x-1$$

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

$$\left(x^{2}-2x-3\right)m=-x-1$$

Whakawehea ngā taha e rua ki te x^{2}-2x-3.

$$\frac{\left(x^{2}-2x-3\right)m}{x^{2}-2x-3}=\frac{-x-1}{x^{2}-2x-3}$$

Mā te whakawehe ki te x^{2}-2x-3 ka wetekia te whakareanga ki te x^{2}-2x-3.

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

Whakawehe -x-1 ki te x^{2}-2x-3.

$$m=-\frac{1}{x-3}$$

Whakaoti mō x

$$\left\{\begin{matrix}\\x=-1\text{, }&\text{unconditionally}\\x=3-\frac{1}{m}\text{, }&m\neq 0\end{matrix}\right.$$