Question:সাধারণ হরবিশিষ্ট ভগ্নাংশে প্রকাশ কর: ২.চ. `1/(x^2 - 5x + 6), 1/(x^2 - 7x + 12), 1/(x^2 - 9x + 20)`
Answer `1/(x^2 - 5x + 6), 1/(x^2 - 7x + 12), 1/(x^2 - 9x + 20)` এখানে, `x^2 - 5x + 6, = x^2 - 3x - 2x + 6` `= x(x - 3) - 2(x - 3)` `= (x - 3) (x - 2)` `x^2 - 7x + 12 = x^2 - 4x - 3x + 12` `= x(x - 4) - 3(x - 4)` `= (x - 4) (x - 3)` `x^2 - 9x + 20 = x^2 - 5x - 4x + 20` `= x(x - 5) - 4(x - 5)` `= (x - 5) (x - 4)` প্রদত্ত ভগ্নাংশগুলোর হর `x^2 - 5x + 6, x^2 - 7x + 12` ও `x^2 - 9x + 20` এর ল,সা,গু `(x - 2) (x - 3) (x - 4) (x - 5)` এখন, হরগুলোর ল,সা,গু/প্রথম ভগ্নাংশের হর `((x - 2)(x - 3)(x - 4)(x - 5))/((x - 3)(x - 2))` `= (x - 4) (x - 5)` `:. 1/(x^2 - 5x + 6)` `= (1(x - 5)(x - 4))/((x - 3)(x - 2)(x - 5)(x - 4))` `= ((x - 4)(x - 5))/((x - 2)(x - 3)(x - 4)(x - 5))` হর গুলোর ল,সা,গু/দ্বিতীয় ভগ্নাংশের হর `((x - 2)(x - 3)(x - 4)(x - 5))/((x - 4)(x - 3))` `= (x - 2) (x - 5)` `:. 1/(x^2 - 7x + 12) = (1(x - 2)(x - 5))/((x - 4)(x - 3) (x - 2)(x - 5))` `= ((x - 2) (x - 5))/((x - 2) (x - 3) (x - 4)(x - 5))` এবং হরগুলোর ল,সা,গু/তৃতীয় ভগ্নাংশের হর `((x - 2)(x - 3)(x - 4)(x - 5))/((x - 5)(x - 4))` `= (x - 2) (x - 3)` `:. 1/(x^2 - 9x + 20) = (1(x - 2)(x - 3))/((x - 5)(x - 4)(x - 2)(x - 3))` `= ((x - 2)(x - 3))/((x - 2)(x - 3)(x - 4)(x - 5)` :. নির্ণেয় সাধারণ হরবিশিষ্ট ভগ্নাংশগুলো হলো `((x - 4)(x - 5))/((x - 2)(x - 3)(x - 4)(x - 5))` `((x - 2)(x - 5))/((x - 2)(x - 3)(x - 4)(x - 5)) ও ((x - 2)(x - 3))/((x - 2) (x - 3)(x - 4)(x - 5))` উত্তর: `((x - 4)(x - 5))/((x - 2)(x - 3)(x - 4)(x - 5)), ((x - 2)(x - 5))/((x - 2)(x - 3)(x - 4)(x - 5))` ও `((x - 2)(x - 3))/((x - 2)(x - 3)(x - 4)(x - 5))`
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shadharon horobishisht bhgnangshe prokasho karo: ২.ch. `1/(x^2 - 5x + 6), 1/(x^2 - 7x + 12), 1/(x^2 - 9x + 20)`