Question:সাধারণ হরবিশিষ্ট ভগ্নাংশে প্রকাশ কর: ২.ঙ. `a/(a^3 + b^3), b/(ab + b^2), c/(a^3 - b^3)`
Answer `a/(a^3 + b^3), b/(a^2 + ab + b^2), c/(a^3 - b^3)` এখানে, `a^3 + b^3 = (a + b) (a^2 - ab + b^2)` `a^2 + ab + b^2 = a^2 + ab + b^2` `a^3 - b^3 = (a - b) (a^2 + ab + b^2)` প্রদত্ত ভগ্নাংশগুলোর হর `a^3 + b^3, a^2 + ab + b^2 ও a^3 - b^3` এর ল,সা,গু `= (a + b) (a^2 - ab + b^2) (a - b) (a^2 + ab + b^2)` এখন, হরগুলোর ল,সা,গু/প্রথম ভগ্নাংশের হর `= ((a + b) (a^2 - ab + b^2) (a - b) (a^2 + ab + b^2))/((a + b) (a^2 - ab + b^2))` `= (a - b) (a^2 + ab + b^2) = a^3 - b^3` `:. a/(a^3 + b^3) = (a(a^3 - b^3))/((a^3 + b^3) (a^3 - b^3)) ` `= (a(a^3 - b^3))/(a^6 - b^6)` হরগুলোর ল,সা,গু/দ্বিতীয় ভগ্নাংশের হর `((a + b) (a^2 - ab + b^2) (a - b) (a^2 + ab + b^2))/(a^2 + ab + b^2)` `= (a + b) (a - b) (a^2 - ab + b^2)` `= (a - b) (a^3 + b^3)` `:. b/(a^2 + ab + b^2)` `= (b(a - b) (a^3 + b^3))/((a - b) (a^3 + b^3) (a^2 + ab + b^2))` `= (b(a - b) (a^3 + b^3))/((a^3 - b^3) (a^3 + b^3)) ` `= (b(a - b)(a^3 + b^3))/(a^6 - b^6)` এবং হরগুলোর ল,সা,গু/তৃতীয় ভগ্নাংশের হর `= ((a + b) (a^2 - ab + b^2)(a - b) (a^2 + ab + b^2))/((a - b)(a^2 + ab + b^2))` `= a^3 + b^3` `:. c/(a^3 - b^3) = (c(a^3 + b^3))/((a^3 - b^3)(a^3 + b^3)) ` `= (c(a^3 + b^3))/(a^6 - b^6)` :. নির্ণেয় সাধারণ হরবিশিষ্ট ভগ্নাংশগুলো হলো `(a(a^3 - b^3))/(a^6 - b^6), (b(a - b)(a^3 + b^3))/(a^6 - b^6) (c(a^3 + b^3))/(a^6 - b^6)` উত্তর: `(a(a^3 - b^3))/(a^6 - b^6), (b(a - b)(a^3 + b^3))/(a^6 - b^6) (c(a^3 + b^3))/(a^6 - b^6)`
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shadharon horobishisht bhgnangshe prokasho karo: ২.ঙ. `a/(a^3 + b^3), b/(ab + b^2), c/(a^3 - b^3)`