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

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

Whakaoti mō m (complex solution)

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

$$x\neq -i\text{ and }x\neq i$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me tāpiri te 3 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

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

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

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

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

Me tāpiri te 2x^{2} ki ngā taha e rua.

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

Tangohia te 2x mai i ngā taha e rua.

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

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

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te x^{2}+1.

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

Mā te whakawehe ki te x^{2}+1 ka wetekia te whakareanga ki te x^{2}+1.

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

Whakaoti mō m

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Me tāpiri te 3 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

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

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

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

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

Me tāpiri te 2x^{2} ki ngā taha e rua.

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

Tangohia te 2x mai i ngā taha e rua.

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

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

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te x^{2}+1.

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

Mā te whakawehe ki te x^{2}+1 ka wetekia te whakareanga ki te x^{2}+1.

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

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{-m^{2}+5m-5}-1}{m-2}\text{; }x=-\frac{\sqrt{-m^{2}+5m-5}+1}{m-2}\text{, }&m\neq 2\\x=\frac{1}{2}\text{, }&m=2\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{\sqrt{-m^{2}+5m-5}-1}{m-2}\text{; }x=-\frac{\sqrt{-m^{2}+5m-5}+1}{m-2}\text{, }&m\neq 2\text{ and }m\geq \frac{5-\sqrt{5}}{2}\text{ and }m\leq \frac{\sqrt{5}+5}{2}\\x=\frac{1}{2}\text{, }&m=2\end{matrix}\right.$$