x-4/x+7+1/3x-2=x-2/x+7 eching

$$\frac { x - 4 } { x + 7 } + \frac { 1 } { 3 x - 2 } = \frac { x - 2 } { x + 7 }$$

x uchun yechish

$$x = \frac{11}{5} = 2\frac{1}{5} = 2,2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -7,\frac{2}{3} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(3x-2\right)\left(x+7\right) ga, x+7,3x-2 ning eng kichik karralisiga ko‘paytiring.

$$\left(3x-2\right)\left(x-4\right)+x+7=\left(3x-2\right)\left(x-2\right)$$

3x-2 ga x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x^{2}-14x+8+x+7=\left(3x-2\right)\left(x-2\right)$$

-13x ni olish uchun -14x va x ni birlashtirish.

$$3x^{2}-13x+8+7=\left(3x-2\right)\left(x-2\right)$$

15 olish uchun 8 va 7'ni qo'shing.

$$3x^{2}-13x+15=\left(3x-2\right)\left(x-2\right)$$

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

$$3x^{2}-13x+15=3x^{2}-8x+4$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$3x^{2}-13x+15-3x^{2}=-8x+4$$

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

$$-13x+15=-8x+4$$

8x ni ikki tarafga qo’shing.

$$-13x+15+8x=4$$

-5x ni olish uchun -13x va 8x ni birlashtirish.

$$-5x+15=4$$

Ikkala tarafdan 15 ni ayirish.

$$-5x=4-15$$

-11 olish uchun 4 dan 15 ni ayirish.

$$-5x=-11$$

Ikki tarafini -5 ga bo‘ling.

$$x=\frac{-11}{-5}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-11}{-5} kasrini \frac{11}{5} ga soddalashtirish mumkin.

$$x=\frac{11}{5}$$