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

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

y uchun yechish

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

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati -2,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(y-2\right)\left(y+2\right) ga, y-2,y+2 ning eng kichik karralisiga ko‘paytiring.

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

y+2 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

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

y-2 ga 16-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan 16y ni ayirish.

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

yx ni ikki tarafga qo’shing.

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

y'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini x^{2}-16+x ga bo‘ling.

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

x^{2}-16+x ga bo'lish x^{2}-16+x ga ko'paytirishni bekor qiladi.

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

-32+2x-2x^{2} ni x^{2}-16+x ga bo'lish.

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

y qiymati -2,2 qiymatlaridan birortasiga teng bo‘lmaydi.

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

x uchun yechish (complex solution)

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

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

x uchun yechish

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

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