Integer and rational expressions
Note as well that the numerator of the second rational expression will be zero. Example 1 Reduce the following rational expression to lowest terms. For example, We simplify a complex rational expression by finding an equivalent fraction where the numerator and denominator are polynomials.
There are some common mistakes that students often make with these problems. Here is the final answer for this part. Moreover, any repeating or terminating decimal represents a rational number. Method 1: Simplify Using Division We begin our discussion on simplifying complex rational expressions using division. Here is the simplification work for this part. A real number that is not rational is called irrational. The goal is to first obtain single algebraic fractions in the numerator and the denominator. The product all the factors from the previous step is the least common denominator. Here is the least common denominator for this rational expression. Write down each factor that appears at least once in any of the denominators. Note as well that to do division of rational expressions all that we need to do is multiply the numerator by the reciprocal of the denominator i.
However, there is a really simple process for finding the least common denominator for rational expressions. It is easy to make a mistake with these and incorrectly do the division. One of them simply has a denominator of one. Here is the simplification work for this part.
In the last term recall that we need to do the multiplication prior to distributing the 3 through the parenthesis. Recall that in order to cancel a factor it must multiply the whole numerator and the whole denominator.
That should always be the first step in these problems.
based on 48 review