Multiplying by an expression
The inequality f(x)<g(x) on a set M, after multiplying both sides by h(x)>0 (on M), keeps the inequality sign; if h(x)<0 — the sign flips to the opposite.
If h changes sign on M, split the domain into intervals where the sign is fixed and solve piecewise.
When h(x)=0, you cannot multiply without a separate analysis of those points
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