1/x-1-2/x-2=1/2x-2-7/3(2x-4) eching

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

x uchun yechish

$$x=-\frac{1}{2}=-0,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 1,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 6\left(x-2\right)\left(x-1\right) ga, x-1,x-2,2x-2,3\left(2x-4\right) ning eng kichik karralisiga ko‘paytiring.

$$6x-12-\left(6x-6\right)\times 2=3x-6-\left(x-1\right)\times 7$$

6x-6 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x-12-\left(12x-12\right)=3x-6-\left(x-1\right)\times 7$$

12x-12 teskarisini topish uchun har birining teskarisini toping.

$$6x-12-12x+12=3x-6-\left(x-1\right)\times 7$$

-6x ni olish uchun 6x va -12x ni birlashtirish.

$$-6x-12+12=3x-6-\left(x-1\right)\times 7$$

0 olish uchun -12 va 12'ni qo'shing.

$$-6x=3x-6-\left(x-1\right)\times 7$$

x-1 ga 7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-6x=3x-6-\left(7x-7\right)$$

7x-7 teskarisini topish uchun har birining teskarisini toping.

$$-6x=3x-6-7x+7$$

-4x ni olish uchun 3x va -7x ni birlashtirish.

$$-6x=-4x-6+7$$

1 olish uchun -6 va 7'ni qo'shing.

$$-6x=-4x+1$$

4x ni ikki tarafga qo’shing.

$$-6x+4x=1$$

-2x ni olish uchun -6x va 4x ni birlashtirish.

$$-2x=1$$

Ikki tarafini -2 ga bo‘ling.

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

\frac{1}{-2} kasri manfiy belgini olib tashlash bilan -\frac{1}{2} sifatida qayta yozilishi mumkin.

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