Rational equations

A rational equation is an equation in which at least one term is a rational expression (a fraction with polynomials in the numerator and denominator). Solving such equations often involves finding a common denominator, clearing denominators, and solving the resulting polynomial equation. Solutions that make any denominator zero must be excluded.

Important properties

• A rational equation may have extraneous solutions—values that solve the transformed equation but make a denominator zero in the original equation.

• Always check potential solutions by substituting back into the original equation.

• The domain of the equation excludes values that make any denominator zero.