Whakaoti i te b^2(x-1)-b(x+5)-6(x+1)=0

$$b ^ { 2 } ( x - 1 ) - b ( x + 5 ) - 6 ( x + 1 ) = 0$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{b+3}{b-3}\text{, }&b\neq 3\\x\in \mathrm{C}\text{, }&b=-2\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te b^{2} ki te x-1.

$$b^{2}x-b^{2}-b\left(x+5\right)-6\left(x+1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te b ki te x+5.

$$b^{2}x-b^{2}-\left(bx+5b\right)-6\left(x+1\right)=0$$

Hei kimi i te tauaro o bx+5b, kimihia te tauaro o ia taurangi.

$$b^{2}x-b^{2}-bx-5b-6\left(x+1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te x+1.

$$b^{2}x-b^{2}-bx-5b-6x-6=0$$

Me tāpiri te b^{2} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$b^{2}x-bx-5b-6x-6=b^{2}$$

Me tāpiri te 5b ki ngā taha e rua.

$$b^{2}x-bx-6x-6=b^{2}+5b$$

Me tāpiri te 6 ki ngā taha e rua.

$$b^{2}x-bx-6x=b^{2}+5b+6$$

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

$$\left(b^{2}-b-6\right)x=b^{2}+5b+6$$

Whakawehea ngā taha e rua ki te b^{2}-b-6.

$$\frac{\left(b^{2}-b-6\right)x}{b^{2}-b-6}=\frac{\left(b+2\right)\left(b+3\right)}{b^{2}-b-6}$$

Mā te whakawehe ki te b^{2}-b-6 ka wetekia te whakareanga ki te b^{2}-b-6.

$$x=\frac{\left(b+2\right)\left(b+3\right)}{b^{2}-b-6}$$

Whakawehe \left(2+b\right)\left(3+b\right) ki te b^{2}-b-6.

$$x=\frac{b+3}{b-3}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{b+3}{b-3}\text{, }&b\neq 3\\x\in \mathrm{R}\text{, }&b=-2\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te b^{2} ki te x-1.

$$b^{2}x-b^{2}-b\left(x+5\right)-6\left(x+1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te b ki te x+5.

$$b^{2}x-b^{2}-\left(bx+5b\right)-6\left(x+1\right)=0$$

Hei kimi i te tauaro o bx+5b, kimihia te tauaro o ia taurangi.

$$b^{2}x-b^{2}-bx-5b-6\left(x+1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te x+1.

$$b^{2}x-b^{2}-bx-5b-6x-6=0$$

Me tāpiri te b^{2} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$b^{2}x-bx-5b-6x-6=b^{2}$$

Me tāpiri te 5b ki ngā taha e rua.

$$b^{2}x-bx-6x-6=b^{2}+5b$$

Me tāpiri te 6 ki ngā taha e rua.

$$b^{2}x-bx-6x=b^{2}+5b+6$$

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

$$\left(b^{2}-b-6\right)x=b^{2}+5b+6$$

Whakawehea ngā taha e rua ki te b^{2}-b-6.

$$\frac{\left(b^{2}-b-6\right)x}{b^{2}-b-6}=\frac{\left(b+2\right)\left(b+3\right)}{b^{2}-b-6}$$

Mā te whakawehe ki te b^{2}-b-6 ka wetekia te whakareanga ki te b^{2}-b-6.

$$x=\frac{\left(b+2\right)\left(b+3\right)}{b^{2}-b-6}$$

Whakawehe \left(2+b\right)\left(3+b\right) ki te b^{2}-b-6.

$$x=\frac{b+3}{b-3}$$

Whakaoti mō b

$$\left\{\begin{matrix}\\b=-2\text{, }&\text{unconditionally}\\b=\frac{3\left(x+1\right)}{x-1}\text{, }&x\neq 1\end{matrix}\right.$$