6m+mn/4mdivn^2-36 eching

$$\frac { 6 m + m n } { 4 m } \div n ^ { 2 } - 36$$

Baholash

$$-36+\frac{1}{4n}+\frac{3}{2n^{2}}$$

Qisqa yechim qadamlari

\frac{\frac{6m+mn}{4m}}{n^{2}} ni yagona kasrga aylantiring.

$$\frac{6m+mn}{4mn^{2}}-36$$

\frac{6m+mn}{4mn^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{m\left(n+6\right)}{4mn^{2}}-36$$

Surat va maxrajdagi ikkala m ni qisqartiring.

$$\frac{n+6}{4n^{2}}-36$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 36 ni \frac{4n^{2}}{4n^{2}} marotabaga ko'paytirish.

$$\frac{n+6}{4n^{2}}-\frac{36\times 4n^{2}}{4n^{2}}$$

\frac{n+6}{4n^{2}} va \frac{36\times 4n^{2}}{4n^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{n+6-36\times 4n^{2}}{4n^{2}}$$

n+6-36\times 4n^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{n+6-144n^{2}}{4n^{2}}$$

\frac{n+6-144n^{2}}{4n^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{-144\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{4n^{2}}$$

Surat va maxrajdagi ikkala 4 ni qisqartiring.

$$\frac{-36\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

-\frac{1}{288}\sqrt{3457}+\frac{1}{288} teskarisini topish uchun har birining teskarisini toping.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

\frac{1}{288}\sqrt{3457}+\frac{1}{288} teskarisini topish uchun har birining teskarisini toping.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

-36 ga n+\frac{1}{288}\sqrt{3457}-\frac{1}{288} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(-36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

-36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8} ga n-\frac{1}{288}\sqrt{3457}-\frac{1}{288} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\left(\sqrt{3457}\right)^{2}-\frac{1}{2304}}{n^{2}}$$

\sqrt{3457} kvadrati – 3457.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\times 3457-\frac{1}{2304}}{n^{2}}$$

\frac{3457}{2304} hosil qilish uchun \frac{1}{2304} va 3457 ni ko'paytirish.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3457}{2304}-\frac{1}{2304}}{n^{2}}$$

\frac{3}{2} olish uchun \frac{3457}{2304} dan \frac{1}{2304} ni ayirish.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3}{2}}{n^{2}}$$

Kengaytirish

$$-36+\frac{1}{4n}+\frac{3}{2n^{2}}$$

Qisqa yechim qadamlari

\frac{\frac{6m+mn}{4m}}{n^{2}} ni yagona kasrga aylantiring.

$$\frac{6m+mn}{4mn^{2}}-36$$

\frac{6m+mn}{4mn^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{m\left(n+6\right)}{4mn^{2}}-36$$

Surat va maxrajdagi ikkala m ni qisqartiring.

$$\frac{n+6}{4n^{2}}-36$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 36 ni \frac{4n^{2}}{4n^{2}} marotabaga ko'paytirish.

$$\frac{n+6}{4n^{2}}-\frac{36\times 4n^{2}}{4n^{2}}$$

\frac{n+6}{4n^{2}} va \frac{36\times 4n^{2}}{4n^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{n+6-36\times 4n^{2}}{4n^{2}}$$

n+6-36\times 4n^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{n+6-144n^{2}}{4n^{2}}$$

\frac{n+6-144n^{2}}{4n^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{-144\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{4n^{2}}$$

Surat va maxrajdagi ikkala 4 ni qisqartiring.

$$\frac{-36\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

-\frac{1}{288}\sqrt{3457}+\frac{1}{288} teskarisini topish uchun har birining teskarisini toping.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

\frac{1}{288}\sqrt{3457}+\frac{1}{288} teskarisini topish uchun har birining teskarisini toping.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

-36 ga n+\frac{1}{288}\sqrt{3457}-\frac{1}{288} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\left(-36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

-36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8} ga n-\frac{1}{288}\sqrt{3457}-\frac{1}{288} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\left(\sqrt{3457}\right)^{2}-\frac{1}{2304}}{n^{2}}$$

\sqrt{3457} kvadrati – 3457.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\times 3457-\frac{1}{2304}}{n^{2}}$$

\frac{3457}{2304} hosil qilish uchun \frac{1}{2304} va 3457 ni ko'paytirish.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3457}{2304}-\frac{1}{2304}}{n^{2}}$$

\frac{3}{2} olish uchun \frac{3457}{2304} dan \frac{1}{2304} ni ayirish.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3}{2}}{n^{2}}$$