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

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

Whakaoti mō m

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

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te m+1 ki te x^{2}.

$$mx^{2}+x^{2}+3x+3=0$$

Tangohia te x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Tangohia te 3x mai i ngā taha e rua.

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

Tangohia te 3 mai i ngā taha e rua.

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

He hanga arowhānui tō te whārite.

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

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

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

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

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

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

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

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{3\left(-4m-1\right)}-3}{2\left(m+1\right)}\text{; }x=-\frac{\sqrt{3}\left(\sqrt{-4m-1}+\sqrt{3}\right)}{2\left(m+1\right)}\text{, }&m\neq -1\\x=-1\text{, }&m=-1\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{\sqrt{3\left(-4m-1\right)}-3}{2\left(m+1\right)}\text{; }x=-\frac{\sqrt{3}\left(\sqrt{-4m-1}+\sqrt{3}\right)}{2\left(m+1\right)}\text{, }&m\neq -1\text{ and }m\leq -\frac{1}{4}\\x=-1\text{, }&m=-1\end{matrix}\right.$$