x+2/x-2-1=8/x^2-4 eching

$$\frac { x + 2 } { x - 2 } - 1 = \frac { 8 } { x ^ { 2 } - 4 }$$

x uchun yechish

$$x=0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -2,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-2\right)\left(x+2\right) ga, x-2,x^{2}-4 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\left(-1\right)=8$$

\left(x+2\right)^{2} hosil qilish uchun x+2 va x+2 ni ko'paytirish.

$$\left(x+2\right)^{2}+\left(x-2\right)\left(x+2\right)\left(-1\right)=8$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+2\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+4x+4+\left(x-2\right)\left(x+2\right)\left(-1\right)=8$$

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

$$x^{2}+4x+4+\left(x^{2}-4\right)\left(-1\right)=8$$

x^{2}-4 ga -1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+4x+4-x^{2}+4=8$$

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

$$4x+4+4=8$$

8 olish uchun 4 va 4'ni qo'shing.

$$4x+8=8$$

Ikkala tarafdan 8 ni ayirish.

$$4x=8-8$$

0 olish uchun 8 dan 8 ni ayirish.

$$4x=0$$

Ikki son koʻpaytmasi 0 ga teng, agar kamida bittasi 0 bo‘lsa. 4 0 ga teng bo‘lmasa, x 0 ga teng bo‘lishi kerak.

$$x=0$$