Issolvi x^2/y-2=4^2-x/y+2

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

Solvi għal y

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

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli y ma jistax ikun ugwali għal kwalunkwe mill-valuri -2,2 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(y-2\right)\left(y+2\right), l-inqas denominatur komuni ta' y-2,y+2.

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

Uża l-propjetà distributtiva biex timmultiplika y+2 b'x^{2}.

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

Ikkalkula 4 bil-power ta' 2 u tikseb 16.

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

Uża l-propjetà distributtiva biex timmultiplika y-2 b'16-x.

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

Naqqas 16y miż-żewġ naħat.

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

Żid yx maż-żewġ naħat.

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

Naqqas 2x^{2} miż-żewġ naħat.

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

Ikkombina t-termini kollha li fihom y.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'x^{2}-16+x.

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

Meta tiddividi b'x^{2}-16+x titneħħa l-multiplikazzjoni b'x^{2}-16+x.

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

Iddividi -32+2x-2x^{2} b'x^{2}-16+x.

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

Il-varjabbli y ma tistax tkun ugwali għal kwalunkwe mill-valuri -2,2.

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

Solvi għal x (complex solution)

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

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

Solvi għal x

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

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