Réitigh x^2/y-2=4^2-x/y+2

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

Réitigh do y.

$$y=-\frac{2\left(x^{2}-x+16\right)}{x^{2}+x-16}$$

$$x\neq 0\text{ and }x\neq \frac{\sqrt{65}-1}{2}\text{ and }x\neq \frac{-\sqrt{65}-1}{2}\text{ and }x\neq 16$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Ní féidir leis an athróg y a bheith comhionann le haon cheann de na luachanna -2,2 toisc nach bhfuil an roinnt faoi nialas sainithe. Iolraigh an dá thaobh den chothromóid faoi \left(y-2\right)\left(y+2\right), an comhiolraí is lú de y-2,y+2.

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

Úsáid an t-airí dáileach chun y+2 a mhéadú faoi x^{2}.

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

Ríomh cumhacht 4 de 2 agus faigh 16.

$$yx^{2}+2x^{2}=\left(y-2\right)\left(16-x\right)$$

Úsáid an t-airí dáileach chun y-2 a mhéadú faoi 16-x.

$$yx^{2}+2x^{2}=16y-yx-32+2x$$

Bain 16y ón dá thaobh.

$$yx^{2}+2x^{2}-16y=-yx-32+2x$$

Cuir yx leis an dá thaobh.

$$yx^{2}+2x^{2}-16y+yx=-32+2x$$

Bain 2x^{2} ón dá thaobh.

$$yx^{2}-16y+yx=-32+2x-2x^{2}$$

Comhcheangail na téarmaí ar fad ina bhfuil y.

$$\left(x^{2}-16+x\right)y=-32+2x-2x^{2}$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(x^{2}+x-16\right)y=-2x^{2}+2x-32$$

Roinn an dá thaobh faoi x^{2}-16+x.

$$\frac{\left(x^{2}+x-16\right)y}{x^{2}+x-16}=\frac{-2x^{2}+2x-32}{x^{2}+x-16}$$

Má roinntear é faoi x^{2}-16+x cuirtear an iolrúchán faoi x^{2}-16+x ar ceal.

$$y=\frac{-2x^{2}+2x-32}{x^{2}+x-16}$$

Roinn -32+2x-2x^{2} faoi x^{2}-16+x.

$$y=\frac{2\left(-x^{2}+x-16\right)}{x^{2}+x-16}$$

Ní féidir leis an athróg y a bheith comhionann le haon cheann de na luachanna -2,2.

$$y=\frac{2\left(-x^{2}+x-16\right)}{x^{2}+x-16}\text{, }y\neq -2\text{ and }y\neq 2$$

Réitigh do x. (complex solution)

$$x=\frac{\sqrt{\left(y-2\right)\left(65y+126\right)}-y+2}{2\left(y+2\right)}$$

$$x=\frac{-\sqrt{\left(y-2\right)\left(65y+126\right)}-y+2}{2\left(y+2\right)}\text{, }y\neq 2\text{ and }y\neq -2$$

Réitigh do x.

$$x=\frac{\sqrt{\left(y-2\right)\left(65y+126\right)}-y+2}{2\left(y+2\right)}$$

$$x=\frac{-\sqrt{\left(y-2\right)\left(65y+126\right)}-y+2}{2\left(y+2\right)}\text{, }y>2\text{ or }\left(y\neq -2\text{ and }y\leq -\frac{126}{65}\right)$$