x-2/x-5=x/x-1 eching

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

x uchun yechish

$$x=-1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 1,5 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-5\right)\left(x-1\right) ga, x-5,x-1 ning eng kichik karralisiga ko‘paytiring.

$$\left(x-1\right)\left(x-2\right)=\left(x-5\right)x$$

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

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

x-5 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-3x+2=x^{2}-5x$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}-3x+2-x^{2}=-5x$$

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

$$-3x+2=-5x$$

5x ni ikki tarafga qo’shing.

$$-3x+2+5x=0$$

2x ni olish uchun -3x va 5x ni birlashtirish.

$$2x+2=0$$

Ikkala tarafdan 2 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$2x=-2$$

Ikki tarafini 2 ga bo‘ling.

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

-1 ni olish uchun -2 ni 2 ga bo‘ling.

$$x=-1$$