A rational expression is an expression that can be written as the ratio of two polynomial expressions. Simplifying rational expressions is an essential skill in algebra, as it allows us to manipulate and solve equations involving fractions.
To simplify a rational expression, we follow a few key steps:
Factor the numerator and denominator: By factoring, we can identify common factors that can be canceled out. For example, consider the expression (3x^2 + 6x) / (2x^2 + 4x). Both the numerator and denominator have a common factor of 3, so we can cancel it out to get (x^2 + 2x) / (2x^2 + 4x).
Cancel common factors: Once we have factored the expression, we can cancel out any common factors in the numerator and denominator. In the previous example, both the numerator and denominator have a common factor of x, so we can cancel it out to simplify the expression further to (x + 2) / (2x + 4).
Dealing with complex fractions: If the expression contains fractions within fractions, we need to simplify them by multiplying the numerator and the denominator by the common denominator of all the fractions involved. For instance, consider the expression (2 / (3x)) / (4 / (5x)). To simplify this complex fraction, we multiply both the numerator and the denominator by the common denominator, which is 3x * 5x, resulting in (2 * 5x) / (4 * 3x).
Remember, the goal of simplifying rational expressions is to make them easier to work with and understand. By factoring, canceling common factors, and handling complex fractions, we can simplify even the most complicated rational expressions.
Keep practicing, and you'll soon be a master at simplifying rational expressions!