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

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

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 \left(x-2\right)\left(x+1\right) ga, x+1,x-2,x^{2}-x-2 ning eng kichik karralisiga ko‘paytiring.

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

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

$$x^{2}-4+\left(x+1\right)\times 3=3+\left(x-2\right)\left(x+1\right)$$

x+1 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-1 olish uchun -4 va 3'ni qo'shing.

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

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

$$x^{2}-1+3x=3+x^{2}-x-2$$

1 olish uchun 3 dan 2 ni ayirish.

$$x^{2}-1+3x=1+x^{2}-x$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}-1+3x-x^{2}=1-x$$

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

$$-1+3x=1-x$$

x ni ikki tarafga qo’shing.

$$-1+3x+x=1$$

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

$$-1+4x=1$$

1 ni ikki tarafga qo’shing.

$$4x=1+1$$

2 olish uchun 1 va 1'ni qo'shing.

$$4x=2$$

Ikki tarafini 4 ga bo‘ling.

$$x=\frac{2}{4}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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