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

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

x uchun yechish

$$x=3$$

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.

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

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

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

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

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

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

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

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

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

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

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

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

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

3x-3 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

Ikkala tarafdan 3x^{2} ni ayirish.

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

0 ni olish uchun 3x^{2} va -3x^{2} ni birlashtirish.

$$-x=-3$$

Ikkala tarafini -1 ga ko‘paytiring.

$$x=3$$