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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,∞)

Exercise: Solve the following inequations

The sets of solutions are:

a) x € (- ∞ , U

b) x € (- ∞ , U

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