1/x+1/y=1/z eching

$$\frac{ 1 }{ x } + \frac{ 1 }{ y } = \frac{ 1 }{ z }$$

x uchun yechish

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

$$y\neq 0\text{ and }z\neq 0\text{ and }y\neq z$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini xyz ga, x,y,z ning eng kichik karralisiga ko‘paytiring.

$$yz+xz=xy$$

Ikkala tarafdan xy ni ayirish.

$$yz+xz-xy=0$$

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

$$xz-xy=-yz$$

Shartlarni qayta saralash.

$$-xy+xz=-yz$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini -y+z ga bo‘ling.

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

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

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

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{yz}{z-y}\text{, }x\neq 0$$

y uchun yechish

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

$$x\neq 0\text{ and }z\neq 0\text{ and }x\neq z$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini xyz ga, x,y,z ning eng kichik karralisiga ko‘paytiring.

$$yz+xz=xy$$

Ikkala tarafdan xy ni ayirish.

$$yz+xz-xy=0$$

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

$$yz-xy=-xz$$

Shartlarni qayta saralash.

$$-xy+yz=-xz$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini z-x ga bo‘ling.

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

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

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

y qiymati 0 teng bo‘lmaydi.

$$y=-\frac{xz}{z-x}\text{, }y\neq 0$$