4/x-1+2/x+1=3/x^2-1 eching

$$\frac { 4 } { x - 1 } + \frac { 2 } { x + 1 } = \frac { 3 } { x ^ { 2 } - 1 }$$

x uchun yechish

$$x=\frac{1}{6}\approx 0,166666667$$

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,x^{2}-1 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+1\right)\times 4+\left(x-1\right)\times 2=3$$

x+1 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x+4+\left(x-1\right)\times 2=3$$

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

$$4x+4+2x-2=3$$

6x ni olish uchun 4x va 2x ni birlashtirish.

$$6x+4-2=3$$

2 olish uchun 4 dan 2 ni ayirish.

$$6x+2=3$$

Ikkala tarafdan 2 ni ayirish.

$$6x=3-2$$

1 olish uchun 3 dan 2 ni ayirish.

$$6x=1$$

Ikki tarafini 6 ga bo‘ling.

$$x=\frac{1}{6}$$