Simplify: $\dfrac{1}{a-1} -\dfrac{1}{a+1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
This is a class 10 Question From Simplification of Rational Expressions chapter of Unit Algebra (Mathematics).
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Solution:
Given,
= $\dfrac{1}{a-1} -\dfrac{1}{a+1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{1(a+1)}{(a-1)(a+1)} -\dfrac{1(a-1)}{(a+1)(a-1)} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{a+1}{a²-1} -\dfrac{a-1}{a²-1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{a+1 -(a-1)}{a²-1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{a+1 -a+1)}{a²-1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{2)}{a²-1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
Given,
= $\dfrac{1}{a-1} -\dfrac{1}{a+1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{1(a+1)}{(a-1)(a+1)} -\dfrac{1(a-1)}{(a+1)(a-1)} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{a+1}{a²-1} -\dfrac{a-1}{a²-1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{a+1 -(a-1)}{a²-1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{a+1 -a+1)}{a²-1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{2)}{a²-1} -\dfrac{2}{a²+1} -\dfrac{4}{a⁴+1}$
= $\dfrac{2(a²+1)}{(a²-1)(a²+1)} -\dfrac{2(a²-1)}{(a²+1)(a²-1)} -\dfrac{4}{a⁴+1}$
= $\dfrac{2a²+2}{(a²-1)(a²+1)} -\dfrac{2a²-2}{(a²+1)(a²-1)} -\dfrac{4}{a⁴+1}$
= $\dfrac{2a²+2-(2a²-2)}{a⁴-1} -\dfrac{4}{a⁴+1}$
= $\dfrac{2a²+2-2a²+2}{a⁴-1} -\dfrac{4}{a⁴+1}$
= $\dfrac{4}{a⁴-1} -\dfrac{4}{a⁴+1}$
= $\dfrac{4(a⁴+1)}{(a⁴-1)(a⁴+1)} -\dfrac{4(a⁴-1)}{(a⁴+1)(a⁴-1)}$
= $\dfrac{4a⁴+4}{a⁸-1} -\dfrac{4a⁴-4}{a⁸-1}$
= $\dfrac{4a⁴+4-(4a⁴-4)}{a⁸-1}$
= $\dfrac{4a⁴+4-4a⁴+4}{a⁸-1}$
= $\dfrac{8}{a⁸-1}$
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Question: Simplify: 1/(a-1) -1/(a+1) -2/(a²+1) -4/(a⁴+1) | SciPiPupil
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