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Equivalence of equations. Theorems on equivalence

Equivalent equations on a set
The equation f(x)=g(x)f(x)=g(x) on a given set MM defines the set of roots — solutions. Two equations are equivalent on MM if their solution sets on MM coincide. The domain of admissible values (DAV) is written down before transformations; when multiplying by fractions — before multiplying, find where denominators are zero.
“Equivalent” without specifying MM usually follows the problem convention (e.g. all reals in the DAV)
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