Whakaoti i te -x^2-ax^2+ax+2x-1=0

$$- x ^ { 2 } - a x ^ { 2 } + a x + 2 x - 1 = 0$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=-1+\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$-x^{2}-ax^{2}+ax-1=-2x$$

Me tāpiri te 1 ki ngā taha e rua.

$$-x^{2}-ax^{2}+ax=-2x+1$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$-ax^{2}+ax=-2x+1+x^{2}$$

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

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

He hanga arowhānui tō te whārite.

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

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

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

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

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

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

$$a=-1+\frac{1}{x}$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-1+\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$-x^{2}-ax^{2}+ax-1=-2x$$

Me tāpiri te 1 ki ngā taha e rua.

$$-x^{2}-ax^{2}+ax=-2x+1$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$-ax^{2}+ax=-2x+1+x^{2}$$

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

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

He hanga arowhānui tō te whārite.

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

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

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

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

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

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

$$a=-1+\frac{1}{x}$$

Whakaoti mō x

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