xy+yz+xz=xyz eching

$$xy+yz+xz=xyz$$

x uchun yechish

$$\left\{\begin{matrix}x=-\frac{yz}{z+y-yz}\text{, }&z=1\text{ or }y\neq -\frac{z}{1-z}\\x\in \mathrm{R}\text{, }&y=0\text{ and }z=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan xyz ni ayirish.

$$xy+yz+xz-xyz=0$$

Ikkala tarafdan yz ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$xy+xz-xyz=-yz$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(y+z-yz\right)x=-yz$$

Tenglama standart shaklda.

$$\left(z+y-yz\right)x=-yz$$

Ikki tarafini y+z-yz ga bo‘ling.

$$\frac{\left(z+y-yz\right)x}{z+y-yz}=-\frac{yz}{z+y-yz}$$

y+z-yz ga bo'lish y+z-yz ga ko'paytirishni bekor qiladi.

$$x=-\frac{yz}{z+y-yz}$$

y uchun yechish

$$\left\{\begin{matrix}y=-\frac{xz}{z+x-xz}\text{, }&z=1\text{ or }x\neq -\frac{z}{1-z}\\y\in \mathrm{R}\text{, }&x=0\text{ and }z=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan xyz ni ayirish.

$$xy+yz+xz-xyz=0$$

Ikkala tarafdan xz ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$xy+yz-xyz=-xz$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x+z-xz\right)y=-xz$$

Tenglama standart shaklda.

$$\left(z+x-xz\right)y=-xz$$

Ikki tarafini x+z-xz ga bo‘ling.

$$\frac{\left(z+x-xz\right)y}{z+x-xz}=-\frac{xz}{z+x-xz}$$

x+z-xz ga bo'lish x+z-xz ga ko'paytirishni bekor qiladi.

$$y=-\frac{xz}{z+x-xz}$$