Question:সাধারণ হরবিশিষ্ট ভগ্নাংশে প্রকাশ কর: 2. ঘ. `(x + y)/(x - y)^2, (x - y)/(x^3 + y^3), (y - z)/(x^2 - y^2)`
Answer ঘ.`(x + y)/(x - y)^2, (x - y)/(x^3 + y^3), (y - z)/(x^2 - y^2)` এখানে, `(x - y)^2 = (x - y) (x - y)` `x^3 + y^3 = (x + y) (x^2 - xy + y^2)` `x^2 - y^2 = (x + y) (x - y)` প্রদত্ত ভগ্নাংশগুলোর হর `(x - y)^2, x^3 + y^3 ও x^2 - y^2` এর ল,সা,গু `(x - y) (x - y) (x + y) (x^2 - xy + y^2)` এখানে, হরগুলোর ল,সা,গু/প্রথম ভগ্নাংশের হর `((x - y)(x - y) (x + y) (x^2 - xy + y^2))/((x - y) (x - y))` `= (x + y) (x^2 - xy + y^2) = x^3 + y^3` `:. (x + y)/(x - y)^2 = ((x + y) (x^3 + y^3))/((x - y)^2 (x^3 + y^3))` হরগুলোর ল,সা,গু/দ্বিতীয় ভগ্নাংশের হর `((x - y) (x - y) (x + y) (x^2 - xy + y^2))/((x + y) (x^2 - xy + y^2))` `= (x - y) (x - y)` `= (x - y)^2` `:. (x - y)/(x^3 + y^3) = ((x - y) (x - y)^2)/((x^3 + y^3) (x - y)^2)` `= ((x - y))^3/((x - y)^2 (x^3 + y^3))` এবং হরগুলোর ল,সা,গু/তৃতীয় ভগ্নাংশের হর `= ((x - y) (x - y) (x + y) (x^2 - xy + y^2))/((x + y) (x - y))` `= (x - y) (x^2 - xy + y^2)` `:. (y - z)/(x^2 - y^2) = ((y - z) (x - y) (x^2 - xy + y^2))/((x^2 - y^2) (x - y) (x^2 - xy + y^2))` `= ((x - y) (y - z) (x^2 - xy + y^2))/((x + y) (x - y) (x - y) (x^2 - xy + y^2))` `= ((x - y) (y - z) (x^2 - xy + y^2))/((x - y)^2 (x^3 + y^3))` :. সাধারণ হরবিশিষ্ট ভগ্নাংশগুলো হলো `((x + y) (x^3 + y^3))/((x - y)^2 (x^3 + y^3)), ((x - y)^3)/((x - y)^2 (x^3 + y^3))` `((x - y) (y - z) (x^2 - xy + y^2))/((x - y)^2 (x^3 + y^3))` উত্তর: `((x + y) (x^3 + y^3))/((x - y)^2 (x^3 + y^3)), ((x - y)^3)/((x - y)^2 (x^3 + y^3))` `((x - y) (y - z) (x^2 - xy + y^2))/((x - y)^2 (x^3 + y^3))`
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shadharon horobishisht bhgnangshe prokasho karo: 2. gh. `(x + y)/(x - y)^2, (x - y)/(x^3 + y^3), (y - z)/(x^2 - y^2)`