[(3u^{2}+14u)(2u^{-3}+u^{-4})]+[(u^3+7u^2-8)(-6u^-4-4u^-5)] eching

$$[ ( 3 u ^ { 2 } + 14 u ) ( 2 u ^ { - 3 } + u ^ { - 4 } ) ] + [ ( u ^ { 3 } + 7 u ^ { 2 } - 8 ) ( - 6 u ^ { - 4 } - 4 u ^ { - 5 } ) ]$$

Baholash

$$\frac{\left(u+2\right)\left(16+16u-15u^{2}\right)}{u^{5}}$$

Yechim qadamlari

3u^{2}+14u ga 2u^{-3}+u^{-4} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6u^{-1}+3u^{2}u^{-4}+28u^{-2}+14uu^{-4}+\left(u^{3}+7u^{2}-8\right)\left(-6u^{-4}-4u^{-5}\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va -4 ni qo‘shib, -2 ni oling.

$$6u^{-1}+3u^{-2}+28u^{-2}+14uu^{-4}+\left(u^{3}+7u^{2}-8\right)\left(-6u^{-4}-4u^{-5}\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va -4 ni qo‘shib, -3 ni oling.

$$6u^{-1}+3u^{-2}+28u^{-2}+14u^{-3}+\left(u^{3}+7u^{2}-8\right)\left(-6u^{-4}-4u^{-5}\right)$$

31u^{-2} ni olish uchun 3u^{-2} va 28u^{-2} ni birlashtirish.

$$6u^{-1}+31u^{-2}+14u^{-3}+\left(u^{3}+7u^{2}-8\right)\left(-6u^{-4}-4u^{-5}\right)$$

u^{3}+7u^{2}-8 ga -6u^{-4}-4u^{-5} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6u^{-1}+31u^{-2}+14u^{-3}-6u^{3}u^{-4}-4u^{3}u^{-5}-42u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va -4 ni qo‘shib, -1 ni oling.

$$6u^{-1}+31u^{-2}+14u^{-3}-6u^{-1}-4u^{3}u^{-5}-42u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va -5 ni qo‘shib, -2 ni oling.

$$6u^{-1}+31u^{-2}+14u^{-3}-6u^{-1}-4u^{-2}-42u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

-46u^{-2} ni olish uchun -4u^{-2} va -42u^{-2} ni birlashtirish.

$$6u^{-1}+31u^{-2}+14u^{-3}-6u^{-1}-46u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

0 ni olish uchun 6u^{-1} va -6u^{-1} ni birlashtirish.

$$31u^{-2}+14u^{-3}-46u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

-15u^{-2} ni olish uchun 31u^{-2} va -46u^{-2} ni birlashtirish.

$$-15u^{-2}+14u^{-3}-28u^{-3}+48u^{-4}+32u^{-5}$$

-14u^{-3} ni olish uchun 14u^{-3} va -28u^{-3} ni birlashtirish.

$$-15u^{-2}-14u^{-3}+48u^{-4}+32u^{-5}$$

Kengaytirish

$$\frac{32+48u-14u^{2}-15u^{3}}{u^{5}}$$

Yechim qadamlari

3u^{2}+14u ga 2u^{-3}+u^{-4} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6u^{-1}+3u^{2}u^{-4}+28u^{-2}+14uu^{-4}+\left(u^{3}+7u^{2}-8\right)\left(-6u^{-4}-4u^{-5}\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va -4 ni qo‘shib, -2 ni oling.

$$6u^{-1}+3u^{-2}+28u^{-2}+14uu^{-4}+\left(u^{3}+7u^{2}-8\right)\left(-6u^{-4}-4u^{-5}\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va -4 ni qo‘shib, -3 ni oling.

$$6u^{-1}+3u^{-2}+28u^{-2}+14u^{-3}+\left(u^{3}+7u^{2}-8\right)\left(-6u^{-4}-4u^{-5}\right)$$

31u^{-2} ni olish uchun 3u^{-2} va 28u^{-2} ni birlashtirish.

$$6u^{-1}+31u^{-2}+14u^{-3}+\left(u^{3}+7u^{2}-8\right)\left(-6u^{-4}-4u^{-5}\right)$$

u^{3}+7u^{2}-8 ga -6u^{-4}-4u^{-5} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6u^{-1}+31u^{-2}+14u^{-3}-6u^{3}u^{-4}-4u^{3}u^{-5}-42u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va -4 ni qo‘shib, -1 ni oling.

$$6u^{-1}+31u^{-2}+14u^{-3}-6u^{-1}-4u^{3}u^{-5}-42u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va -5 ni qo‘shib, -2 ni oling.

$$6u^{-1}+31u^{-2}+14u^{-3}-6u^{-1}-4u^{-2}-42u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

-46u^{-2} ni olish uchun -4u^{-2} va -42u^{-2} ni birlashtirish.

$$6u^{-1}+31u^{-2}+14u^{-3}-6u^{-1}-46u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

0 ni olish uchun 6u^{-1} va -6u^{-1} ni birlashtirish.

$$31u^{-2}+14u^{-3}-46u^{-2}-28u^{-3}+48u^{-4}+32u^{-5}$$

-15u^{-2} ni olish uchun 31u^{-2} va -46u^{-2} ni birlashtirish.

$$-15u^{-2}+14u^{-3}-28u^{-3}+48u^{-4}+32u^{-5}$$

-14u^{-3} ni olish uchun 14u^{-3} va -28u^{-3} ni birlashtirish.

$$-15u^{-2}-14u^{-3}+48u^{-4}+32u^{-5}$$