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

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

x uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$\left(x-2\right)\left(x-3\right)=\left(x+1\right)\left(x+4\right)$$

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

$$x^{2}-5x+6=\left(x+1\right)\left(x+4\right)$$

x+1 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

Ikkala tarafdan x^{2} ni ayirish.

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

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

$$-5x+6=5x+4$$

Ikkala tarafdan 5x ni ayirish.

$$-5x+6-5x=4$$

-10x ni olish uchun -5x va -5x ni birlashtirish.

$$-10x+6=4$$

Ikkala tarafdan 6 ni ayirish.

$$-10x=4-6$$

-2 olish uchun 4 dan 6 ni ayirish.

$$-10x=-2$$

Ikki tarafini -10 ga bo‘ling.

$$x=\frac{-2}{-10}$$

\frac{-2}{-10} ulushini -2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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