Since the square of any real number is nonnegative, x^2 is nonnegative. Then x^2 + 1 is the sum
of the nonnegative quantity x^2 and the positive quantity 1. So x^2 + 1 is positive. The fraction
will be negative when the numerator 1 − 5x is negative. Solve the inequality 1 − 5x < 0:
Thus, the fraction will be negative when and only when .