Simplify:
1/u^2-2u-1/u^2-4
Please Show All Work!
To simplify the expression (1/u^2 - 2u - 1)/(u^2 - 4), we'll need to factor the numerator and denominator to see if anything cancels out.
First, let's factor the numerator:
1/u^2 - 2u - 1 = (1 - u^3)(1 + u)
Next, let's factor the denominator using the difference of squares formula:
u^2 - 4 = (u - 2)(u + 2)
Now we have:
(1 - u^3)(1 + u) / (u - 2)(u + 2)
Since there are no common factors between the numerator and denominator, we cannot cancel out anything further. Therefore, the simplified form of the expression is (1 - u^3)(1 + u) / (u - 2)(u + 2).