Whakaoti i te (x-10)(x-1)--(x+1)(x-y)=6

$$(x-10)(x-1)--(x+1)(x-y)=6$$

Whakaoti mō y

$$y=\frac{2\left(x^{2}-5x+2\right)}{x+1}$$

$$x\neq -1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tuaritanga hei whakarea te x-10 ki te x-1 ka whakakotahi i ngā kupu rite.

$$x^{2}-11x+10-\left(-\left(x+1\right)\right)\left(x-y\right)=6$$

Hei kimi i te tauaro o x+1, kimihia te tauaro o ia taurangi.

$$x^{2}-11x+10-\left(-x-1\right)\left(x-y\right)=6$$

Whakamahia te āhuatanga tohatoha hei whakarea te -x-1 ki te x-y.

$$x^{2}-11x+10-\left(-x^{2}+xy-x+y\right)=6$$

Hei kimi i te tauaro o -x^{2}+xy-x+y, kimihia te tauaro o ia taurangi.

$$x^{2}-11x+10+x^{2}-xy+x-y=6$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}-11x+10-xy+x-y=6$$

Pahekotia te -11x me x, ka -10x.

$$2x^{2}-10x+10-xy-y=6$$

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

$$-10x+10-xy-y=6-2x^{2}$$

Me tāpiri te 10x ki ngā taha e rua.

$$10-xy-y=6-2x^{2}+10x$$

Tangohia te 10 mai i ngā taha e rua.

$$-xy-y=6-2x^{2}+10x-10$$

Tangohia te 10 i te 6, ka -4.

$$-xy-y=-4-2x^{2}+10x$$

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

$$\left(-x-1\right)y=-4-2x^{2}+10x$$

He hanga arowhānui tō te whārite.

$$\left(-x-1\right)y=-2x^{2}+10x-4$$

Whakawehea ngā taha e rua ki te -x-1.

$$\frac{\left(-x-1\right)y}{-x-1}=\frac{-2x^{2}+10x-4}{-x-1}$$

Mā te whakawehe ki te -x-1 ka wetekia te whakareanga ki te -x-1.

$$y=\frac{-2x^{2}+10x-4}{-x-1}$$

Whakawehe -4-2x^{2}+10x ki te -x-1.

$$y=-\frac{2\left(-x^{2}+5x-2\right)}{x+1}$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{y^{2}+28y+68}+y+10}{4}$$

$$x=\frac{-\sqrt{y^{2}+28y+68}+y+10}{4}$$

Whakaoti mō x

$$x=\frac{\sqrt{y^{2}+28y+68}+y+10}{4}$$

$$x=\frac{-\sqrt{y^{2}+28y+68}+y+10}{4}\text{, }y\geq 8\sqrt{2}-14\text{ or }y\leq -8\sqrt{2}-14$$