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

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

x uchun yechish

$$x=4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -2,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+2\right) ga, x+2,x-1 ning eng kichik karralisiga ko‘paytiring.

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

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

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

x-1 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

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

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

-4 olish uchun -2 dan 2 ni ayirish.

$$3x-4+x^{2}=\left(x+2\right)x$$

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

$$3x-4+x^{2}=x^{2}+2x$$

Ikkala tarafdan x^{2} ni ayirish.

$$3x-4+x^{2}-x^{2}=2x$$

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

$$3x-4=2x$$

Ikkala tarafdan 2x ni ayirish.

$$3x-4-2x=0$$

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

$$x-4=0$$

4 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x=4$$