Question

What should be added to $\frac{1}{x-2}+\frac{1}{x+2}$ to get $\frac{4x^3}{x^4-16}$ ?

Answer 1

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Let A be the required value.

$\frac{1}{x-2}+\frac{1}{x+2}+A=\frac{4x^3}{x^4-16}$

$A=\frac{4x^3}{x^4-16}-\frac{2x}{x^2-4}$

$A=\frac{2x}{x^2-4}\left[\frac{2x^2-x^2-4}{x^2+4}\right]$

$A=\frac{2x}{x^2+4}$

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