Solving Inequalities Involving Quotients of Polynomials

To solve an inequality of the formmoving everyhing over to one side, simplify and analyse sign changes for each factor in numerator and denominator.

For this example, moving eveything to the left hand side gives

Simplifying by adding as fractions gives

Changes of sign for each factor are summarised in the following diagram, and for the whole expression- the bottom line, labelled).

forand x>2. This is illustrated for original question in the diagram below.