Solving integer rational inequalities (interval method for linear factors)

What an "integer rational" inequality is

In the school course an integer rational inequality is usually written as

\dfrac{P(x)}{Q(x)}\gtrless 0

(or

\geq,\leq

), where

P,Q

are polynomials and the denominator is not zero on the solution set (domain of admissible values — DAV). A special case without a fraction:

P(x)>0

— effectively

Q(x)=1

. The sign-chart method after factoring into linear factors (and tracking a constant sign separately) lets you mark the sign of the product on each interval between roots and points of discontinuity.

First move everything to one side and factor numerator and denominator into factors like

(x-x_i)

Points where a factor of odd multiplicity changes sign are the "flip" points of the sign chart

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