2/3[4a-3b)+1/3b-1/4(6a+7b)] eching

$$\frac { 2 } { 3 } [ 4 a - 3 b ) + \frac { 1 } { 3 } b - \frac { 1 } { 4 } ( 6 a + 7 b ) ]$$

Baholash

$$\frac{7a}{6}-\frac{41b}{12}$$

Yechim qadamlari

\frac{2}{3} ga 4a-3b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2}{3}\times 4a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

\frac{2}{3}\times 4 ni yagona kasrga aylantiring.

$$\frac{2\times 4}{3}a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$\frac{8}{3}a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

\frac{2}{3}\left(-3\right) ni yagona kasrga aylantiring.

$$\frac{8}{3}a+\frac{2\left(-3\right)}{3}b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

-6 hosil qilish uchun 2 va -3 ni ko'paytirish.

$$\frac{8}{3}a+\frac{-6}{3}b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

-2 ni olish uchun -6 ni 3 ga bo‘ling.

$$\frac{8}{3}a-2b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

-\frac{5}{3}b ni olish uchun -2b va \frac{1}{3}b ni birlashtirish.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{1}{4}\left(6a+7b\right)$$

-\frac{1}{4} ga 6a+7b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{1}{4}\times 6a-\frac{1}{4}\times 7b$$

-\frac{1}{4}\times 6 ni yagona kasrga aylantiring.

$$\frac{8}{3}a-\frac{5}{3}b+\frac{-6}{4}a-\frac{1}{4}\times 7b$$

\frac{-6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a-\frac{1}{4}\times 7b$$

-\frac{1}{4}\times 7 ni yagona kasrga aylantiring.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a+\frac{-7}{4}b$$

\frac{-7}{4} kasri manfiy belgini olib tashlash bilan -\frac{7}{4} sifatida qayta yozilishi mumkin.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a-\frac{7}{4}b$$

\frac{7}{6}a ni olish uchun \frac{8}{3}a va -\frac{3}{2}a ni birlashtirish.

$$\frac{7}{6}a-\frac{5}{3}b-\frac{7}{4}b$$

-\frac{41}{12}b ni olish uchun -\frac{5}{3}b va -\frac{7}{4}b ni birlashtirish.

$$\frac{7}{6}a-\frac{41}{12}b$$

Kengaytirish

$$\frac{7a}{6}-\frac{41b}{12}$$

Yechim qadamlari

\frac{2}{3} ga 4a-3b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2}{3}\times 4a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

\frac{2}{3}\times 4 ni yagona kasrga aylantiring.

$$\frac{2\times 4}{3}a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$\frac{8}{3}a+\frac{2}{3}\left(-3\right)b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

\frac{2}{3}\left(-3\right) ni yagona kasrga aylantiring.

$$\frac{8}{3}a+\frac{2\left(-3\right)}{3}b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

-6 hosil qilish uchun 2 va -3 ni ko'paytirish.

$$\frac{8}{3}a+\frac{-6}{3}b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

-2 ni olish uchun -6 ni 3 ga bo‘ling.

$$\frac{8}{3}a-2b+\frac{1}{3}b-\frac{1}{4}\left(6a+7b\right)$$

-\frac{5}{3}b ni olish uchun -2b va \frac{1}{3}b ni birlashtirish.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{1}{4}\left(6a+7b\right)$$

-\frac{1}{4} ga 6a+7b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{1}{4}\times 6a-\frac{1}{4}\times 7b$$

-\frac{1}{4}\times 6 ni yagona kasrga aylantiring.

$$\frac{8}{3}a-\frac{5}{3}b+\frac{-6}{4}a-\frac{1}{4}\times 7b$$

\frac{-6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a-\frac{1}{4}\times 7b$$

-\frac{1}{4}\times 7 ni yagona kasrga aylantiring.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a+\frac{-7}{4}b$$

\frac{-7}{4} kasri manfiy belgini olib tashlash bilan -\frac{7}{4} sifatida qayta yozilishi mumkin.

$$\frac{8}{3}a-\frac{5}{3}b-\frac{3}{2}a-\frac{7}{4}b$$

\frac{7}{6}a ni olish uchun \frac{8}{3}a va -\frac{3}{2}a ni birlashtirish.

$$\frac{7}{6}a-\frac{5}{3}b-\frac{7}{4}b$$

-\frac{41}{12}b ni olish uchun -\frac{5}{3}b va -\frac{7}{4}b ni birlashtirish.

$$\frac{7}{6}a-\frac{41}{12}b$$