Equations and inequalities with Rational Functions

Rational equations and inequalities

To solve equations involving rational expressions, we have the freedom to clear out fractions before proceeding. After multiplying both sides by the common denominator, we are left with a polynomial equation.

One solution of the equation is . Find another solution.


When faced with nonlinear inequalities, such as those involving general rational functions, we make use of a sign chart. The inequality in the following example is not given in factored form, so we have some work to do.

Find the solution of the inequality: .
none of the above