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

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

x uchun yechish

$$x=\frac{9}{13}\approx 0,692307692$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -2,\frac{1}{3} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(3x-1\right)\left(x+2\right) ga, x+2,3x-1 ning eng kichik karralisiga ko‘paytiring.

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

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

$$3x^{2}-10x+3+\left(x+2\right)\left(3x+1\right)=2\left(3x-1\right)\left(x+2\right)$$

x+2 ga 3x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x^{2}-10x+3+3x^{2}+7x+2=2\left(3x-1\right)\left(x+2\right)$$

6x^{2} ni olish uchun 3x^{2} va 3x^{2} ni birlashtirish.

$$6x^{2}-10x+3+7x+2=2\left(3x-1\right)\left(x+2\right)$$

-3x ni olish uchun -10x va 7x ni birlashtirish.

$$6x^{2}-3x+3+2=2\left(3x-1\right)\left(x+2\right)$$

5 olish uchun 3 va 2'ni qo'shing.

$$6x^{2}-3x+5=2\left(3x-1\right)\left(x+2\right)$$

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

$$6x^{2}-3x+5=\left(6x-2\right)\left(x+2\right)$$

6x-2 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$6x^{2}-3x+5=6x^{2}+10x-4$$

Ikkala tarafdan 6x^{2} ni ayirish.

$$6x^{2}-3x+5-6x^{2}=10x-4$$

0 ni olish uchun 6x^{2} va -6x^{2} ni birlashtirish.

$$-3x+5=10x-4$$

Ikkala tarafdan 10x ni ayirish.

$$-3x+5-10x=-4$$

-13x ni olish uchun -3x va -10x ni birlashtirish.

$$-13x+5=-4$$

Ikkala tarafdan 5 ni ayirish.

$$-13x=-4-5$$

-9 olish uchun -4 dan 5 ni ayirish.

$$-13x=-9$$

Ikki tarafini -13 ga bo‘ling.

$$x=\frac{-9}{-13}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-9}{-13} kasrini \frac{9}{13} ga soddalashtirish mumkin.

$$x=\frac{9}{13}$$