3/x+1=x/x-1-1 eching

$$\frac{ 3 }{ x+1 } = \frac{ x }{ x-1 } -1$$

x uchun yechish

$$x=2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+1\right) ga, x+1,x-1 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-1\right)\times 3=\left(x+1\right)x+\left(x-1\right)\left(x+1\right)\left(-1\right)$$

x-1 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-3=\left(x+1\right)x+\left(x-1\right)\left(x+1\right)\left(-1\right)$$

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

$$3x-3=x^{2}+x+\left(x-1\right)\left(x+1\right)\left(-1\right)$$

x-1 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x-3=x^{2}+x+\left(x^{2}-1\right)\left(-1\right)$$

x^{2}-1 ga -1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-3=x^{2}+x-x^{2}+1$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$3x-3=x+1$$

Ikkala tarafdan x ni ayirish.

$$3x-3-x=1$$

2x ni olish uchun 3x va -x ni birlashtirish.

$$2x-3=1$$

3 ni ikki tarafga qo’shing.

$$2x=1+3$$

4 olish uchun 1 va 3'ni qo'shing.

$$2x=4$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{4}{2}$$

2 ni olish uchun 4 ni 2 ga bo‘ling.

$$x=2$$