x+6/x^2-4+1/x+2=2/x-2 eching

$$\frac{ x+6 }{ { x }^{ 2 } -4 } + \frac{ 1 }{ x+2 } = \frac{ 2 }{ x-2 }$$

x uchun yechish (complex solution)

$$x\in \mathrm{C}\setminus -2,2$$

Yechim qadamlari

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}-4,x+2,x-2 ning eng kichik karralisiga ko‘paytiring.

$$x+6+x-2=\left(x+2\right)\times 2$$

2x ni olish uchun x va x ni birlashtirish.

$$2x+6-2=\left(x+2\right)\times 2$$

4 olish uchun 6 dan 2 ni ayirish.

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

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

$$2x+4=2x+4$$

Ikkala tarafdan 2x ni ayirish.

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

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

$$4=4$$

4 va 4 ni taqqoslang.

$$\text{true}$$

Bu har qanday x uchun to‘g‘ri.

$$x\in \mathrm{C}$$

x qiymati -2,2 qiymatlaridan birortasiga teng bo‘lmaydi.

$$x\in \mathrm{C}\setminus -2,2$$

x uchun yechish

$$x\in \mathrm{R}\setminus 2,-2$$

Yechim qadamlari

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}-4,x+2,x-2 ning eng kichik karralisiga ko‘paytiring.

$$x+6+x-2=\left(x+2\right)\times 2$$

2x ni olish uchun x va x ni birlashtirish.

$$2x+6-2=\left(x+2\right)\times 2$$

4 olish uchun 6 dan 2 ni ayirish.

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

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

$$2x+4=2x+4$$

Ikkala tarafdan 2x ni ayirish.

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

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

$$4=4$$

4 va 4 ni taqqoslang.

$$\text{true}$$

Bu har qanday x uchun to‘g‘ri.

$$x\in \mathrm{R}$$

x qiymati -2,2 qiymatlaridan birortasiga teng bo‘lmaydi.

$$x\in \mathrm{R}\setminus -2,2$$