### Instruction: Solve
\[\frac{x + 6}{x^2 + 2x + 7} \ge 0.\]Enter your answer using interval notation.### Response: I notice that the denominator of the fraction is always positive, since it is a quadratic expression with no real roots and a positive leading coefficient.
This means that the sign of the fraction depends only on the sign of the numerator, x + 6.
So I want to find the values of x that make x + 6 non-negative, or x + 6 >= 0.
Subtracting 6 from both sides, I get x >= -6.
This means that the fraction is non-negative for all x greater than or equal to -6.
In interval notation, this is written as [-6, infinity).