R
Rishtaara
Algebra & Precalculus
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.