Multiplying & Dividing Rational Expressions

In this section, we review how to multiply and divide rational expressions. For the topic of multiplication with rational expressions, we think back to when we multiplied with fractions. Essentially, we first want to factor each polynomial in the numerator along with each polynomial in the denominator. We then cancel any common factors between numerator and denominator along with cross canceling between the numerator of one rational expression and the denominator of the other. Once we have canceled as many common factors as possible, we multiply numerators together and place the result over the product of the denominators. When we divide with rational expressions, we again follow the same technique as we used when we divided with fractions. We want to keep the first rational expression the same (either topmost or left most depending on formatting). We then find the reciprocal of the second rational expression (either the rational expression on the bottom or the one on the right, depending on the formatting). Once this is done, we cancel any common factors and find the product.