2x+5/x-3=1/3+4/x-3 eching

$$\frac{ 2x+5 }{ x-3 } = \frac{ 1 }{ 3 } + \frac{ 4 }{ x-3 }$$

x uchun yechish

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1,2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3\left(x-3\right) ga, x-3,3 ning eng kichik karralisiga ko‘paytiring.

$$3\left(2x+5\right)=3\left(x-3\right)\times \frac{1}{3}+3\times 4$$

3 ga 2x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x+15=3\left(x-3\right)\times \frac{1}{3}+3\times 4$$

1 hosil qilish uchun 3 va \frac{1}{3} ni ko'paytirish.

$$6x+15=x-3+3\times 4$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$6x+15=x-3+12$$

9 olish uchun -3 va 12'ni qo'shing.

$$6x+15=x+9$$

Ikkala tarafdan x ni ayirish.

$$6x+15-x=9$$

5x ni olish uchun 6x va -x ni birlashtirish.

$$5x+15=9$$

Ikkala tarafdan 15 ni ayirish.

$$5x=9-15$$

-6 olish uchun 9 dan 15 ni ayirish.

$$5x=-6$$

Ikki tarafini 5 ga bo‘ling.

$$x=\frac{-6}{5}$$

\frac{-6}{5} kasri manfiy belgini olib tashlash bilan -\frac{6}{5} sifatida qayta yozilishi mumkin.

$$x=-\frac{6}{5}$$