Whakaoti i te (x+3)(x+m)=x

$$( x + 3 ) ( x + m ) = x$$

Whakaoti mō m

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

$$x\neq -3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x+3 ki te x+m.

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

Tangohia te x^{2} mai i ngā taha e rua.

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

Tangohia te 3x mai i ngā taha e rua.

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

Pahekotia te x me -3x, ka -2x.

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

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

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te x+3.

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

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

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

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{m^{2}-8m+4}}{2}-\frac{m}{2}-1$$

$$x=-\frac{\sqrt{m^{2}-8m+4}}{2}-\frac{m}{2}-1$$

Whakaoti mō x

$$x=\frac{\sqrt{m^{2}-8m+4}}{2}-\frac{m}{2}-1$$

$$x=-\frac{\sqrt{m^{2}-8m+4}}{2}-\frac{m}{2}-1\text{, }m\geq 2\sqrt{3}+4\text{ or }m\leq 4-2\sqrt{3}$$