Question

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

Answer 1

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

Explanation:

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`.