rational inequalities/Domain

Question

 explain why (x^2+2) / (x^2+1) < 0 has no solution

Answer 1

For every x, x² is positive, and therefore x² + 2 is positive.

The numerator is always positive.

For the same reasons the denominator is always positive.

The division (fraction) of two positives is positive.

It cannot be negative, < 0.