In order to simplify complex rational expressions, it is important to be able to find the lowest common denominator. Complex rational expressions are fractions that are divided by fractions. When you have found the lowest common denominator, then, you should multiply both fractions by the common denominator. With 4/x divided by 3/y, the common denominator it xy. Therefore, you should multiply the top and bottom by xy. Then, simplify the expression. This will give you 4y/3x. Regardless of how complicated the problem is the process will always be exactly the same as this simple problem. Look at all of the denominators. Then, figure out what the lowest common denominator is. Then, multiply all of the equations by the common denominator. Then, simplify it. Then, solve it. Make sure it's in its simplest form.