Mathematics

The key is to treat this like a sign analysis: factor the numerator, identify where the expression equals zero (zeros) and where it's undefined (poles), then test the sign in each region. Remember that zeros make the expression equal to zero (included in $\geq$), while poles create vertical asymptotes (always excluded). By organizing these critical points on a number line and checking one test point in each interval, you'll see exactly where the rational expression stays non-negative.

The key is to treat this like a sign analysis: factor the numerator, identify where the expression equals zero (zeros) and where it's undefined (poles), then test the sign in each region. Remember that zeros make the expression equal to zero (included in $\geq$), while poles create vertical asymptotes (always excluded). By organizing these critical points on a number line and checking one test point in each interval, you'll see exactly where the rational expression stays non-negative.