Rational inequations

To solve a rational inequation:
- Obtain an equivalent inequation with only a fraction in one side and 0 in the other.
- Find the roots of the polynomials in the numerator and denominator.
- The solutions divide the real number line into pieces. Then, try one value from each piece and, if the inequation is true, the whole piece is a solution.
- Try the roots of the numerator and write the whole solution.

Example 1:

  Then, the solution is x€ (-∞,2]U(4,∞)

  Example 2:

    Then the solution is:  x € (- ∞,2)U(7,∞)