2mn/m^3+n^3+2m/m^2-n^2-1/m-n eching

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

Baholash

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

Qisqa yechim qadamlari

Faktor: m^{3}+n^{3}. Faktor: m^{2}-n^{2}.

$$\frac{2mn}{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}+\frac{2m}{\left(m+n\right)\left(m-n\right)}-\frac{1}{m-n}$$

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

$$\frac{2mn\left(m-n\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}+\frac{2m\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{1}{m-n}$$

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

$$\frac{2mn\left(m-n\right)+2m\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{1}{m-n}$$

2mn\left(m-n\right)+2m\left(m^{2}-mn+n^{2}\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2m^{2}n-2mn^{2}+2m^{3}-2m^{2}n+2mn^{2}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{1}{m-n}$$

2m^{2}n-2mn^{2}+2m^{3}-2m^{2}n+2mn^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{2m^{3}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)}-\frac{1}{m-n}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right) va m-n ning eng kichik umumiy karralisi \left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right). \frac{1}{m-n} ni \frac{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)} marotabaga ko'paytirish.

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

\frac{2m^{3}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)} va \frac{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

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

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

2m^{3}-m^{3}+m^{2}n-mn^{2}-nm^{2}+n^{2}m-n^{3} kabi iboralarga o‘xshab birlashtiring.

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

\frac{m^{3}-n^{3}}{\left(m+n\right)\left(m-n\right)\left(m^{2}-mn+n^{2}\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala m-n ni qisqartiring.

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

\left(m+n\right)\left(m^{2}-mn+n^{2}\right) ni kengaytirish.

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

m ga nisbatan hosilani topish

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