3x+4/x^2+x-2=4/x-1+5/x+2 eching

$$\frac { 3 x + 4 } { x ^ { 2 } + x - 2 } = \frac { 4 } { x - 1 } + \frac { 5 } { x + 2 }$$

x uchun yechish

$$x=\frac{1}{6}\approx 0,166666667$$

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-2,x-1,x+2 ning eng kichik karralisiga ko‘paytiring.

$$3x+4=\left(x+2\right)\times 4+\left(x-1\right)\times 5$$

x+2 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x+4=4x+8+\left(x-1\right)\times 5$$

x-1 ga 5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x+4=4x+8+5x-5$$

9x ni olish uchun 4x va 5x ni birlashtirish.

$$3x+4=9x+8-5$$

3 olish uchun 8 dan 5 ni ayirish.

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

Ikkala tarafdan 9x ni ayirish.

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

-6x ni olish uchun 3x va -9x ni birlashtirish.

$$-6x+4=3$$

Ikkala tarafdan 4 ni ayirish.

$$-6x=3-4$$

-1 olish uchun 3 dan 4 ni ayirish.

$$-6x=-1$$

Ikki tarafini -6 ga bo‘ling.

$$x=\frac{-1}{-6}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-1}{-6} kasrini \frac{1}{6} ga soddalashtirish mumkin.

$$x=\frac{1}{6}$$