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

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

x uchun yechish

$$x = -\frac{7}{3} = -2\frac{1}{3} \approx -2,333333333$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

\left(x+1\right)^{2} hosil qilish uchun x+1 va x+1 ni ko'paytirish.

$$\left(x+1\right)^{2}=\left(x+2\right)\left(x-3\right)$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+2x+1=\left(x+2\right)\left(x-3\right)$$

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

$$x^{2}+2x+1=x^{2}-x-6$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}+2x+1-x^{2}=-x-6$$

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

$$2x+1=-x-6$$

x ni ikki tarafga qo’shing.

$$2x+1+x=-6$$

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

$$3x+1=-6$$

Ikkala tarafdan 1 ni ayirish.

$$3x=-6-1$$

-7 olish uchun -6 dan 1 ni ayirish.

$$3x=-7$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{-7}{3}$$

\frac{-7}{3} kasri manfiy belgini olib tashlash bilan -\frac{7}{3} sifatida qayta yozilishi mumkin.

$$x=-\frac{7}{3}$$