Whakaoti i te (a-b)x^2=2bx+4a

$$( a - b ) x ^ { 2 } = 2 b x + 4 a$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bx}{2-x}\text{, }&x\neq 2\\a\in \mathrm{C}\text{, }&x=-2\text{ or }\left(b=0\text{ and }x=2\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a-b ki te x^{2}.

$$ax^{2}-bx^{2}=2bx+4a$$

Tangohia te 4a mai i ngā taha e rua.

$$ax^{2}-bx^{2}-4a=2bx$$

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

$$ax^{2}-4a=2bx+bx^{2}$$

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

$$\left(x^{2}-4\right)a=2bx+bx^{2}$$

He hanga arowhānui tō te whārite.

$$\left(x^{2}-4\right)a=bx^{2}+2bx$$

Whakawehea ngā taha e rua ki te x^{2}-4.

$$\frac{\left(x^{2}-4\right)a}{x^{2}-4}=\frac{bx\left(x+2\right)}{x^{2}-4}$$

Mā te whakawehe ki te x^{2}-4 ka wetekia te whakareanga ki te x^{2}-4.

$$a=\frac{bx\left(x+2\right)}{x^{2}-4}$$

Whakawehe bx\left(2+x\right) ki te x^{2}-4.

$$a=\frac{bx}{x-2}$$

Whakaoti mō b (complex solution)

$$\left\{\begin{matrix}b=\frac{a\left(x-2\right)}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&x=-2\text{ or }\left(a=0\text{ and }x=0\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a-b ki te x^{2}.

$$ax^{2}-bx^{2}=2bx+4a$$

Tangohia te 2bx mai i ngā taha e rua.

$$ax^{2}-bx^{2}-2bx=4a$$

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

$$-bx^{2}-2bx=4a-ax^{2}$$

Whakaraupapatia anō ngā kīanga tau.

$$-bx^{2}-2bx=-ax^{2}+4a$$

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

$$\left(-x^{2}-2x\right)b=-ax^{2}+4a$$

He hanga arowhānui tō te whārite.

$$\left(-x^{2}-2x\right)b=4a-ax^{2}$$

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

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

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

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

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

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

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{bx}{2-x}\text{, }&x\neq 2\\a\in \mathrm{R}\text{, }&x=-2\text{ or }\left(b=0\text{ and }x=2\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a-b ki te x^{2}.

$$ax^{2}-bx^{2}=2bx+4a$$

Tangohia te 4a mai i ngā taha e rua.

$$ax^{2}-bx^{2}-4a=2bx$$

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

$$ax^{2}-4a=2bx+bx^{2}$$

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

$$\left(x^{2}-4\right)a=2bx+bx^{2}$$

He hanga arowhānui tō te whārite.

$$\left(x^{2}-4\right)a=bx^{2}+2bx$$

Whakawehea ngā taha e rua ki te x^{2}-4.

$$\frac{\left(x^{2}-4\right)a}{x^{2}-4}=\frac{bx\left(x+2\right)}{x^{2}-4}$$

Mā te whakawehe ki te x^{2}-4 ka wetekia te whakareanga ki te x^{2}-4.

$$a=\frac{bx\left(x+2\right)}{x^{2}-4}$$

Whakawehe bx\left(2+x\right) ki te x^{2}-4.

$$a=\frac{bx}{x-2}$$

Whakaoti mō b

$$\left\{\begin{matrix}b=\frac{a\left(x-2\right)}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=-2\text{ or }\left(a=0\text{ and }x=0\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a-b ki te x^{2}.

$$ax^{2}-bx^{2}=2bx+4a$$

Tangohia te 2bx mai i ngā taha e rua.

$$ax^{2}-bx^{2}-2bx=4a$$

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

$$-bx^{2}-2bx=4a-ax^{2}$$

Whakaraupapatia anō ngā kīanga tau.

$$-bx^{2}-2bx=-ax^{2}+4a$$

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

$$\left(-x^{2}-2x\right)b=-ax^{2}+4a$$

He hanga arowhānui tō te whārite.

$$\left(-x^{2}-2x\right)b=4a-ax^{2}$$

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

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

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

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

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

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