Question:`p = 1/(x - 1), q = 2/(x^2 + 1), r = 4/(x^4 + 1), s = 1/(x + 1)` হলে ক. (p + q) নির্ণয় কর। খ. `1/p, 1/q, 1/s`এর ল,সা,গু নির্ণয় কর। গ. (p - s - q + r) কে সরল কর।
Answer ক. দেওয়া আছে, `p = 1/(x - 1), q = 2/(x^2 + 1)` `:. p + p = 1/(x - 1) + 2/(x^2 + 1)` `= (x^2 + 1 + 2 (x - 1))/((x - 1)(x^2 + 1))` `= (x^2 + 1 + 2x - 2)/((x - 1) (x^2 + 1)` `= (x^2 + 2x - 1)/((x - 1) (x^2 + 1))` (Ans) খ. দেওয়া আছে, `p = 1/(x - 1)` `:. 1/p = x - 1` `q = 2/(x^2 + 1)` `x^2 + 1 = 2/q` `(x^2 + 1)/2 = 1/q` `:. 1/q = (x^2 + 1)/2` `s = 1/(x + 1)` `:. 1/s = x + 1` `:. 1/p, 1/q` এবং `1/s` এর ল,সা,গু 1. গ. দেওয়া আছে, `p = 1/(x - 1), q = 2/(x^2 + 1), r = 4/(x^4 + 1)` এবং `s = 1/(x + 1)` `:. p - s - q + r = 1/(x - 1) - 1/(x + 1) - 2/(x^2 + 1) + 4/(x^4 + 1)` `= (x + 1 - x + 1)/(x^2 - 1) - 2/(x^2 + 1) + 4/(x^4 + 1)` `= 2/(x^2 - 1) - 2/(x^2 + 1) + 4/(x^4 + 1)` `= (2 (x^2 + 1) - 2 (x^2 - 1))/((x^2 - 1) (x^2 + 1)) + 4/(x^4 + 1)` `= (2x^2 + 2 - 2x^2 + 2)/(x^4 - 1) + 4/(x^4 + 1)` `= 4/(x^4 - 1) + 1/(x^4 + 1)` `= (4x^4 + 4 + 4x^4 - 4)/((x^4 - 1)(x^4 + 1))` `= (8x^4)/(x^8 - 1)` (Ans)
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`p = 1/(x - 1), q = 2/(x^2 + 1), r = 4/(x^4 + 1), s = 1/(x + 1)` hole ka. (p + q) nirony karo. kh. `1/p, 1/q, 1/s`ar l,sha,gu nirony karo. ga. (p - s - q + r) ke shorol karo.