Lesson 4 of 12Article17 min
Rational & Radical Equations
Clear denominators by multiplying through by the LCD. Always exclude values that make any original denominator zero — check for extraneous solutions.
Rational equations
Clear denominators by multiplying through by the LCD. Always exclude values that make any original denominator zero — check for extraneous solutions.
- Asymptotes: vertical where Q=0 (after cancelling), horizontal from degree comparison.
- Holes: cancelled factors create removable discontinuities.
Radical equations
Isolate the radical, then raise both sides to the matching power. Check every candidate in the original — squaring can invent extras.
√(something) is never negative in the real numbers. That alone kills many false roots.