Simplify: x⁴/(x²+1) +x⁴/(x²-1) -1/(x²+1) -1/(x²-1) | SciPiPupil

Simplify: $\dfrac{x⁴}{x²+1} +\dfrac{x⁴}{x²-1} -\dfrac{1}{x²+1} -\dfrac{1}{x²-1}$

This is a class 10 Question From Simplification of Rational Expressions chapter of Unit Algebra (Mathematics).  

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Solution:

Given,

= $\dfrac{x⁴}{x²+1} +\dfrac{x⁴}{x²-1} -\dfrac{1}{x²+1} -\dfrac{1}{x²-1}$

= $\dfrac{x⁴}{x²+1} -\dfrac{1}{x²+1} +\dfrac{x⁴}{x²-1} -\dfrac{1}{x²-1}$

= $\dfrac{x⁴-1}{x²+1} +\dfrac{x⁴-1}{x²-1}$

= $\dfrac{(x²)²-1²}{x²+1} +\dfrac{(x²)²-1²}{x²-1}$

= $\dfrac{(x²+1)(x²-1)}{x²+1} +\dfrac{(x²+1)(x²-1)}{x²-1}$

= $x²-1 +x²+1$

= $2x²$

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Question: Simplify: x⁴/(x²+1) +x⁴/(x²-1) -1/(x²+1) -1/(x²-1) | SciPiPupil

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