(frac{8k^{2}}{3+4k^2})^2-44k^2+12/3+4k^2 eching

$$( \frac { 8 k ^ { 2 } } { 3 + 4 k ^ { 2 } } ) ^ { 2 } - 4 \frac { 4 k ^ { 2 } + 12 } { 3 + 4 k ^ { 2 } }$$

Baholash

$$-\frac{48\left(5k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

Qisqa yechim qadamlari

\frac{8k^{2}}{3+4k^{2}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(8k^{2}\right)^{2}}{\left(3+4k^{2}\right)^{2}}-4\times \frac{4k^{2}+12}{3+4k^{2}}$$

4\times \frac{4k^{2}+12}{3+4k^{2}} ni yagona kasrga aylantiring.

$$\frac{\left(8k^{2}\right)^{2}}{\left(3+4k^{2}\right)^{2}}-\frac{4\left(4k^{2}+12\right)}{3+4k^{2}}$$

4 ga 4k^{2}+12 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(8k^{2}\right)^{2}}{\left(3+4k^{2}\right)^{2}}-\frac{16k^{2}+48}{3+4k^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(3+4k^{2}\right)^{2} va 3+4k^{2} ning eng kichik umumiy karralisi \left(4k^{2}+3\right)^{2}. \frac{16k^{2}+48}{3+4k^{2}} ni \frac{4k^{2}+3}{4k^{2}+3} marotabaga ko'paytirish.

$$\frac{\left(8k^{2}\right)^{2}}{\left(4k^{2}+3\right)^{2}}-\frac{\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

\frac{\left(8k^{2}\right)^{2}}{\left(4k^{2}+3\right)^{2}} va \frac{\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\left(8k^{2}\right)^{2}-\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

\left(8k^{2}\right)^{2} ni kengaytirish.

$$\frac{8^{2}\left(k^{2}\right)^{2}}{\left(3+4k^{2}\right)^{2}}-\frac{16k^{2}+48}{3+4k^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

$$\frac{8^{2}k^{4}}{\left(3+4k^{2}\right)^{2}}-\frac{16k^{2}+48}{3+4k^{2}}$$

2 daraja ko‘rsatkichini 8 ga hisoblang va 64 ni qiymatni oling.

$$\frac{64k^{4}}{\left(3+4k^{2}\right)^{2}}-\frac{16k^{2}+48}{3+4k^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(3+4k^{2}\right)^{2} va 3+4k^{2} ning eng kichik umumiy karralisi \left(4k^{2}+3\right)^{2}. \frac{16k^{2}+48}{3+4k^{2}} ni \frac{4k^{2}+3}{4k^{2}+3} marotabaga ko'paytirish.

$$\frac{64k^{4}}{\left(4k^{2}+3\right)^{2}}-\frac{\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

\frac{64k^{4}}{\left(4k^{2}+3\right)^{2}} va \frac{\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{64k^{4}-\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

64k^{4}-\left(16k^{2}+48\right)\left(4k^{2}+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{64k^{4}-64k^{4}-48k^{2}-192k^{2}-144}{\left(4k^{2}+3\right)^{2}}$$

64k^{4}-64k^{4}-48k^{2}-192k^{2}-144 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-240k^{2}-144}{\left(4k^{2}+3\right)^{2}}$$

\left(4k^{2}+3\right)^{2} ni kengaytirish.

$$\frac{-240k^{2}-144}{16k^{4}+24k^{2}+9}$$

Kengaytirish

$$-\frac{48\left(5k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

Qisqa yechim qadamlari

\frac{8k^{2}}{3+4k^{2}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(8k^{2}\right)^{2}}{\left(3+4k^{2}\right)^{2}}-4\times \frac{4k^{2}+12}{3+4k^{2}}$$

4\times \frac{4k^{2}+12}{3+4k^{2}} ni yagona kasrga aylantiring.

$$\frac{\left(8k^{2}\right)^{2}}{\left(3+4k^{2}\right)^{2}}-\frac{4\left(4k^{2}+12\right)}{3+4k^{2}}$$

4 ga 4k^{2}+12 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(8k^{2}\right)^{2}}{\left(3+4k^{2}\right)^{2}}-\frac{16k^{2}+48}{3+4k^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(3+4k^{2}\right)^{2} va 3+4k^{2} ning eng kichik umumiy karralisi \left(4k^{2}+3\right)^{2}. \frac{16k^{2}+48}{3+4k^{2}} ni \frac{4k^{2}+3}{4k^{2}+3} marotabaga ko'paytirish.

$$\frac{\left(8k^{2}\right)^{2}}{\left(4k^{2}+3\right)^{2}}-\frac{\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

\frac{\left(8k^{2}\right)^{2}}{\left(4k^{2}+3\right)^{2}} va \frac{\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\left(8k^{2}\right)^{2}-\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

\left(8k^{2}\right)^{2} ni kengaytirish.

$$\frac{8^{2}\left(k^{2}\right)^{2}}{\left(3+4k^{2}\right)^{2}}-\frac{16k^{2}+48}{3+4k^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

$$\frac{8^{2}k^{4}}{\left(3+4k^{2}\right)^{2}}-\frac{16k^{2}+48}{3+4k^{2}}$$

2 daraja ko‘rsatkichini 8 ga hisoblang va 64 ni qiymatni oling.

$$\frac{64k^{4}}{\left(3+4k^{2}\right)^{2}}-\frac{16k^{2}+48}{3+4k^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(3+4k^{2}\right)^{2} va 3+4k^{2} ning eng kichik umumiy karralisi \left(4k^{2}+3\right)^{2}. \frac{16k^{2}+48}{3+4k^{2}} ni \frac{4k^{2}+3}{4k^{2}+3} marotabaga ko'paytirish.

$$\frac{64k^{4}}{\left(4k^{2}+3\right)^{2}}-\frac{\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

\frac{64k^{4}}{\left(4k^{2}+3\right)^{2}} va \frac{\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{64k^{4}-\left(16k^{2}+48\right)\left(4k^{2}+3\right)}{\left(4k^{2}+3\right)^{2}}$$

64k^{4}-\left(16k^{2}+48\right)\left(4k^{2}+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{64k^{4}-64k^{4}-48k^{2}-192k^{2}-144}{\left(4k^{2}+3\right)^{2}}$$

64k^{4}-64k^{4}-48k^{2}-192k^{2}-144 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-240k^{2}-144}{\left(4k^{2}+3\right)^{2}}$$

\left(4k^{2}+3\right)^{2} ni kengaytirish.

$$\frac{-240k^{2}-144}{16k^{4}+24k^{2}+9}$$