Whakaoti i te a(x-3)(x-1)=1

$$a ( x - 3 ) ( x - 1 ) = 1$$

Whakaoti mō a

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

$$x\neq 1\text{ and }x\neq 3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a ki te x-3.

$$\left(ax-3a\right)\left(x-1\right)=1$$

Whakamahia te āhuatanga tuaritanga hei whakarea te ax-3a ki te x-1 ka whakakotahi i ngā kupu rite.

$$ax^{2}-4ax+3a=1$$

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

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

Whakawehea ngā taha e rua ki te x^{2}-4x+3.

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

Mā te whakawehe ki te x^{2}-4x+3 ka wetekia te whakareanga ki te x^{2}-4x+3.

$$a=\frac{1}{x^{2}-4x+3}$$

Whakawehe 1 ki te x^{2}-4x+3.

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

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{a^{2}+a}}{a}+2$$

$$x=-\frac{\sqrt{a^{2}+a}}{a}+2\text{, }a\neq 0$$

Whakaoti mō x

$$x=\frac{\sqrt{a^{2}+a}}{a}+2$$

$$x=-\frac{\sqrt{a^{2}+a}}{a}+2\text{, }a>0\text{ or }a\leq -1$$