2n/n+2n+m/2n-m+4mn/4n^2-n^2 eching

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

Baholash

$$\frac{4n^{2}+9mn-4m^{2}}{3n\left(2n-m\right)}$$

Qisqa yechim qadamlari

3n ni olish uchun n va 2n ni birlashtirish.

$$\frac{2n}{3n}+\frac{m}{2n-m}+\frac{4mn}{4n^{2}-n^{2}}$$

Surat va maxrajdagi ikkala n ni qisqartiring.

$$\frac{2}{3}+\frac{m}{2n-m}+\frac{4mn}{4n^{2}-n^{2}}$$

3n^{2} ni olish uchun 4n^{2} va -n^{2} ni birlashtirish.

$$\frac{2}{3}+\frac{m}{2n-m}+\frac{4mn}{3n^{2}}$$

Surat va maxrajdagi ikkala n ni qisqartiring.

$$\frac{2}{3}+\frac{m}{2n-m}+\frac{4m}{3n}$$

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

$$\frac{2\left(-m+2n\right)}{3\left(-m+2n\right)}+\frac{3m}{3\left(-m+2n\right)}+\frac{4m}{3n}$$

\frac{2\left(-m+2n\right)}{3\left(-m+2n\right)} va \frac{3m}{3\left(-m+2n\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\left(-m+2n\right)+3m}{3\left(-m+2n\right)}+\frac{4m}{3n}$$

2\left(-m+2n\right)+3m ichidagi ko‘paytirishlarni bajaring.

$$\frac{-2m+4n+3m}{3\left(-m+2n\right)}+\frac{4m}{3n}$$

-2m+4n+3m kabi iboralarga o‘xshab birlashtiring.

$$\frac{m+4n}{3\left(-m+2n\right)}+\frac{4m}{3n}$$

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

$$\frac{\left(m+4n\right)n}{3n\left(-m+2n\right)}+\frac{4m\left(-m+2n\right)}{3n\left(-m+2n\right)}$$

\frac{\left(m+4n\right)n}{3n\left(-m+2n\right)} va \frac{4m\left(-m+2n\right)}{3n\left(-m+2n\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(m+4n\right)n+4m\left(-m+2n\right)}{3n\left(-m+2n\right)}$$

\left(m+4n\right)n+4m\left(-m+2n\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{mn+4n^{2}-4m^{2}+8mn}{3n\left(-m+2n\right)}$$

mn+4n^{2}-4m^{2}+8mn kabi iboralarga o‘xshab birlashtiring.

$$\frac{-4m^{2}+9mn+4n^{2}}{3n\left(-m+2n\right)}$$

3n\left(-m+2n\right) ni kengaytirish.

$$\frac{-4m^{2}+9mn+4n^{2}}{-3mn+6n^{2}}$$

m ga nisbatan hosilani topish

$$\frac{2\left(-2m^{2}+8mn-11n^{2}\right)}{3n\left(m-2n\right)\left(2n-m\right)}$$