Anonymous

LHS denominator = x^2+3x+11 has no real roots so LHS is always positive

Anonymous

Making assumptions about where parentheses should be, 2/(x^2 + 3x + 11) = 2/(x^2 + 3x + 9/4 + 35/4) = 2/((x + 3/2)^2 + 35/4) The numerator and denominator are positive for all real x so 2/(x^2 + 3x + 11) > 0 for all real x

Anonymous

Assuming you mean: 2/(x^2+3x+11) < 0 the up opening quadratic associated with the denominator has no real roots. Thus it can not be < 0. Therefore the rational form can not be < 0.