y=x+1/x-1 eching

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

x uchun yechish

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

$$y\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-1 ga ko'paytirish.

$$y\left(x-1\right)=x+1$$

y ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$yx-y=x+1$$

Ikkala tarafdan x ni ayirish.

$$yx-y-x=1$$

y ni ikki tarafga qo’shing.

$$yx-x=1+y$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(y-1\right)x=1+y$$

Tenglama standart shaklda.

$$\left(y-1\right)x=y+1$$

Ikki tarafini y-1 ga bo‘ling.

$$\frac{\left(y-1\right)x}{y-1}=\frac{y+1}{y-1}$$

y-1 ga bo'lish y-1 ga ko'paytirishni bekor qiladi.

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

x qiymati 1 teng bo‘lmaydi.

$$x=\frac{y+1}{y-1}\text{, }x\neq 1$$

y uchun yechish

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

$$x\neq 1$$