What is \( \Large \frac{1}{a-b} \)-\( \Large \frac{1}{a+b} \)-\( \Large \frac{2b}{a^{2}+b^{2}} \)-\( \Large \frac{4b^{3}}{a^{4}+b^{4}} \)-\( \Large \frac{8b^{7}}{a^{8}-b^{8}} \)
Correct Answer: Description for Correct answer:
\( \Large \frac{1}{a - b} - \frac{1}{a + b} + \frac{2b}{a^{2} + b^{2}} - \frac{4b^{3}}{a^{4} + b^{4}} - \frac{8b^{7}}{a^{8} - b^{8}}\)
let a = b
and b = 0
\( \Large \frac{1}{1} - \frac{1}{1} - 0 - 0 - 0 = 0 \)
Now from option(a)
\( \Large a + b = 1 + 0 = 1 \ne 0 \)
option (A)is wrong
From option (B)
\( \Large a -b = 1 - 0 = 1 \ne 0 \)
option (B)is wrong
From option (C)
\( \Large 1 \ne 0 \)
option (C)is wrong
and Option (D)is correct.
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