Math Rational Inequalities Definition

The process for solving rational inequalities is nearly identical to the process for solving polynomial inequalities with a few minor differences.

Math rational inequalities definition. Example for x 4 the rational expression x 2 2x 13 x 2 x 3 11 6. A rational expression looks like. The key approach in solving rational inequalities relies on finding the critical values of the rational expression which divide the number line into distinct open intervals. Inequalities describe a relationship between two values that are not equal.

Hence the rational expression on the left side of the given inequality is negative on the interval 3. Solving rational inequalities rational. Re write the problem if necessary to obtain a zero on one side. Example greater than.

A rational inequality is an inequality which contains a rational expression. The sign of the rational expression on the left side of the given inequality will change at all the zeros because they all have odd multiplicity. The rational expression will have the same sign as the sign at the test point since it can only change sign at those points. The critical values are simply the zeros of both the numerator and the denominator.

Math explained in easy language plus puzzles games quizzes worksheets and a forum. Let s just jump straight into some examples. Hide ads about ads. To solve a rational inequality you first find the zeroes from the numerator and the undefined points from the denominator.

A b states that the value of a is less than the value of b and a b states that the value of a is greater than the value of b. But because rational expressions have denominators and therefore may have places where they re not defined you have to be a little more careful in finding your solutions. You must remember that the zeros of the denominator make the rational expression undefined so they must be immediately disregarded or excluded as a possible solution. Sometimes we need to solve rational inequalities like these.

For k 12 kids teachers and parents. The trick to dealing with rational inequalities is to always work with zero on one side of the inequality. Just as we did with polynomial inequalities all we need to do is check the rational expression at test points in each region between the points from the previous step.