The Method of intervals (or wavy curve) is used for solving inequalities of the form f(x) =
> 0 ( 0, or > 0) where n1, n2, ……, nk, m1, m2, ……, mp are natural numbers and the numbers a1, a2, ……, ak; b1, b2,……, bp are any real numbers such that ai ¹ bj, where i = 1, 2, 3, ……, k and j = 1, 2, 3, ……, p.
q All zeros1 of the function f(x) contained on the left hand side of the inequality should be marked on the number line with inked (black) circles.
q All points of discontinuities2 of the function f(x) contained on the left hand side of the inequality should be marked on the number line with un-inked (white) circles.
q Check the value of f(x) for any real number greater than the right most marked number on the number line.
q From right to left, beginning above the number line (in case of value of f(x) is positive in step (iii), otherwise, from below the number line), a wavy curve should be drawn to pass through all the marked points so that when it passes through a simple point3, the curve intersects the number line, and, when passing through a double point4, the curve remains located on one side of the number line.
q The appropriate intervals are chosen in accordance with the sign of inequality (the function f(x) is positive whenever the curve is situated above the number line, it is negative if the curve is found below the number line). Their union represents the solution of inequality.

Remark:
(i) Points of discontinuity will never be included in the answer.
(ii) If you are asked to find the intervals where f(x) is non-negative or non-positive then make the intervals closed corresponding to the roots of the numerator and let it remain open corresponding to the roots of denominator.
1The point for which f(x) vanishes (becomes zero) are called zeros of function e.g. x = ai.
2The points x = bj are the point of the discontinuity of the function f(x).
3If the exponents of a factor is odd then the point is called a simple point.
4If the exponent of a factor is even then the point is called a double point.