How to solve fractional inequalities

How to solve fractional inequalities

Fractional inequalities demand to themselves more attentive relation, than usual inequalities as in certain cases in the course of the decision the sign changes. Fractional inequalities are solved by method of intervals.


1. Present fractional inequality so that on the one hand there was fractional rational expression, and on other side of the sign - 0. Now inequality in a general view looks so: f (x)/g (x)> (<, ≤ or ≥) 0.

2. Define points in which g(x) changes the sign, write down all intervals on which g (x) a znakopostoyanna.

3. For each interval present initial fractional expression in the form of performing the f (x) and g (x) functions, changing the sign of inequality, when necessary. Actually you multiply the right and left part of inequality by the same number. At the same time the sign of inequality changes on opposite if the number (in our case of g (x)) is negative and remains to the same if the number is positive. Also at the same time the severity (>, <) and not severity (≤, ≥) inequalities remains.

4. To the received inequality of f (x) *g(x)> (<, ≤ or ≥) 0 apply standard methods of the decision, but now to each interval of a numerical straight line found earlier. The same method of intervals of a znakopostoyanstvo applied to function f will be one of them (x).

Author: «MirrorInfo» Dream Team