Whakaoti i te 1/x-1/2-x=-a

$$\frac { 1 } { x } - \frac { 1 } { 2 - x } = - a$$

Whakaoti mō a

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

$$x\neq 0\text{ and }x\neq 2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te x\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,2-x.

$$x-2+x=-x\left(x-2\right)a$$

Pahekotia te x me x, ka 2x.

$$2x-2=-x\left(x-2\right)a$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-2.

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

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

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

Hei kimi i te tauaro o x^{2}a-2xa, kimihia te tauaro o ia taurangi.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

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

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

He hanga arowhānui tō te whārite.

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

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

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

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

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

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

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

Whakaoti mō x

$$\left\{\begin{matrix}x=-\frac{\sqrt{a^{2}+1}-a+1}{a}\text{; }x=\frac{\sqrt{a^{2}+1}+a-1}{a}\text{, }&a\neq 0\\x=1\text{, }&a=0\end{matrix}\right.$$