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

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

x uchun yechish

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1,666666667$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

$$x^{2}-3x-4=\left(x+3\right)\left(x-3\right)$$

Hisoblang: \left(x+3\right)\left(x-3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$x^{2}-3x-4=x^{2}-9$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}-3x-4-x^{2}=-9$$

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

$$-3x-4=-9$$

4 ni ikki tarafga qo’shing.

$$-3x=-9+4$$

-5 olish uchun -9 va 4'ni qo'shing.

$$-3x=-5$$

Ikki tarafini -3 ga bo‘ling.

$$x=\frac{-5}{-3}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-5}{-3} kasrini \frac{5}{3} ga soddalashtirish mumkin.

$$x=\frac{5}{3}$$