1/r-2+1/r^2-7r+10=6/r-2 eching

$$\frac { 1 } { r - 2 } + \frac { 1 } { r ^ { 2 } - 7 r + 10 } = \frac { 6 } { r - 2 }$$

r uchun yechish

$$r = \frac{26}{5} = 5\frac{1}{5} = 5,2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

r qiymati 2,5 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(r-5\right)\left(r-2\right) ga, r-2,r^{2}-7r+10 ning eng kichik karralisiga ko‘paytiring.

$$r-5+1=\left(r-5\right)\times 6$$

-4 olish uchun -5 va 1'ni qo'shing.

$$r-4=\left(r-5\right)\times 6$$

r-5 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$r-4=6r-30$$

Ikkala tarafdan 6r ni ayirish.

$$r-4-6r=-30$$

-5r ni olish uchun r va -6r ni birlashtirish.

$$-5r-4=-30$$

4 ni ikki tarafga qo’shing.

$$-5r=-30+4$$

-26 olish uchun -30 va 4'ni qo'shing.

$$-5r=-26$$

Ikki tarafini -5 ga bo‘ling.

$$r=\frac{-26}{-5}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-26}{-5} kasrini \frac{26}{5} ga soddalashtirish mumkin.

$$r=\frac{26}{5}$$