How do you divide $u^2 /( u^2-4)$ ?

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Answer 1 · 2015-12-16T14:47:52

$u^2/(u^2 - 4) = 1 + 4/(u^2 - 4)$

In this case, it's easiest not to perform the polynomial long division, but rather to extend the numerator:

$u^2/(u^2-4) = (u^2 color(blue)(-4 + 4))/(u^2-4) = (u^2 - 4)/(u^2 - 4) + 4/(u^2 - 4) = 1 + 4/(u^2 - 4)$

In other words, $u^2 -: (u^2-4) = 1$ with remainder $4$ .

How do you divide u^2 /( u^2-4)u^2 /( u^2-4)?