4/k+1+5/k=3/k eching

$$\frac { 4 } { k + 1 } + \frac { 5 } { k } = \frac { 3 } { k }$$

k uchun yechish

$$k=-\frac{1}{3}\approx -0,333333333$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k qiymati -1,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini k\left(k+1\right) ga, k+1,k ning eng kichik karralisiga ko‘paytiring.

$$k\times 4+\left(k+1\right)\times 5=\left(k+1\right)\times 3$$

k+1 ga 5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$k\times 4+5k+5=\left(k+1\right)\times 3$$

9k ni olish uchun k\times 4 va 5k ni birlashtirish.

$$9k+5=\left(k+1\right)\times 3$$

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

$$9k+5=3k+3$$

Ikkala tarafdan 3k ni ayirish.

$$9k+5-3k=3$$

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

$$6k+5=3$$

Ikkala tarafdan 5 ni ayirish.

$$6k=3-5$$

-2 olish uchun 3 dan 5 ni ayirish.

$$6k=-2$$

Ikki tarafini 6 ga bo‘ling.

$$k=\frac{-2}{6}$$

\frac{-2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$k=-\frac{1}{3}$$