Whakaoti i te x/a+1/2a=2x-3/2a+2(1-a)

$$\frac { x } { a } + \frac { 1 } { 2 } a = 2 x - \frac { 3 } { 2 } a + 2 ( 1 - a )$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=2a\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&a=\frac{1}{2}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 2a, arā, te tauraro pātahi he tino iti rawa te kitea o a,2.

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

Whakareatia te a ki te a, ka a^{2}.

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

Whakareatia te \frac{1}{2} ki te 2, ka 1.

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

Whakareatia te a ki te a, ka a^{2}.

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

Whakareatia te 2 ki te 2, ka 4.

$$2x+a^{2}=4xa-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Whakareatia te -\frac{3}{2} ki te 2, ka -3.

$$2x+a^{2}=4xa-3a^{2}+2\left(1-a\right)\times 2a$$

Whakareatia te 2 ki te 2, ka 4.

$$2x+a^{2}=4xa-3a^{2}+4\left(1-a\right)a$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 1-a.

$$2x+a^{2}=4xa-3a^{2}+\left(4-4a\right)a$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4-4a ki te a.

$$2x+a^{2}=4xa-3a^{2}+4a-4a^{2}$$

Pahekotia te -3a^{2} me -4a^{2}, ka -7a^{2}.

$$2x+a^{2}=4xa-7a^{2}+4a$$

Tangohia te 4xa mai i ngā taha e rua.

$$2x+a^{2}-4xa=-7a^{2}+4a$$

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

$$2x-4xa=-7a^{2}+4a-a^{2}$$

Pahekotia te -7a^{2} me -a^{2}, ka -8a^{2}.

$$2x-4xa=-8a^{2}+4a$$

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

$$\left(2-4a\right)x=-8a^{2}+4a$$

He hanga arowhānui tō te whārite.

$$\left(2-4a\right)x=4a-8a^{2}$$

Whakawehea ngā taha e rua ki te 2-4a.

$$\frac{\left(2-4a\right)x}{2-4a}=\frac{4a\left(1-2a\right)}{2-4a}$$

Mā te whakawehe ki te 2-4a ka wetekia te whakareanga ki te 2-4a.

$$x=\frac{4a\left(1-2a\right)}{2-4a}$$

Whakawehe 4a\left(1-2a\right) ki te 2-4a.

$$x=2a$$

Whakaoti mō x

$$\left\{\begin{matrix}x=2a\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&a=\frac{1}{2}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 2a, arā, te tauraro pātahi he tino iti rawa te kitea o a,2.

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

Whakareatia te a ki te a, ka a^{2}.

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

Whakareatia te \frac{1}{2} ki te 2, ka 1.

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

Whakareatia te a ki te a, ka a^{2}.

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

Whakareatia te 2 ki te 2, ka 4.

$$2x+a^{2}=4xa-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Whakareatia te -\frac{3}{2} ki te 2, ka -3.

$$2x+a^{2}=4xa-3a^{2}+2\left(1-a\right)\times 2a$$

Whakareatia te 2 ki te 2, ka 4.

$$2x+a^{2}=4xa-3a^{2}+4\left(1-a\right)a$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 1-a.

$$2x+a^{2}=4xa-3a^{2}+\left(4-4a\right)a$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4-4a ki te a.

$$2x+a^{2}=4xa-3a^{2}+4a-4a^{2}$$

Pahekotia te -3a^{2} me -4a^{2}, ka -7a^{2}.

$$2x+a^{2}=4xa-7a^{2}+4a$$

Tangohia te 4xa mai i ngā taha e rua.

$$2x+a^{2}-4xa=-7a^{2}+4a$$

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

$$2x-4xa=-7a^{2}+4a-a^{2}$$

Pahekotia te -7a^{2} me -a^{2}, ka -8a^{2}.

$$2x-4xa=-8a^{2}+4a$$

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

$$\left(2-4a\right)x=-8a^{2}+4a$$

He hanga arowhānui tō te whārite.

$$\left(2-4a\right)x=4a-8a^{2}$$

Whakawehea ngā taha e rua ki te 2-4a.

$$\frac{\left(2-4a\right)x}{2-4a}=\frac{4a\left(1-2a\right)}{2-4a}$$

Mā te whakawehe ki te 2-4a ka wetekia te whakareanga ki te 2-4a.

$$x=\frac{4a\left(1-2a\right)}{2-4a}$$

Whakawehe 4a\left(1-2a\right) ki te 2-4a.

$$x=2a$$

Whakaoti mō a

$$\left\{\begin{matrix}\\a=\frac{1}{2}=0.5\text{, }&\text{unconditionally}\\a=\frac{x}{2}\text{, }&x\neq 0\end{matrix}\right.$$