Lesson Summary: By the end of this lesson, students should understand the three different types of partial fraction decomposition depending on the factor that lies in the denominator. One should know that to solve rational inequalities, one should use sign diagrams and follow all of the necessary steps learned in the previous lesson. However, on the number line, one should also plot the vertical asymptotes as well. Finally, one should be able to solve rational equations by first finding the LCD and finding the domain, multiplying both sides of the equation by the LCD to get rid of the denominator, solving the remaining equation, and finally, checking for extraneous solutions according to the domain.