Now, we can add the numerators as the denominators are the same. To make the denominators the same, we multiply and divide the first fraction by (x + 1). Here, the LCD (leat common denominator) is x (x + 1). The given rational expressions can be written as (3 / x) + Now, we can add/subtract all the numerators as now the denominators are the same.Įxample: Add the rational expressions (3 / x) + (1 / (x 2 + x)).Multiply and divide each rational expression by some expression/number such that all the denominators are same as LCD found in the above step.Find the LCD (LCM) of their denominators.In general, to add/subtract two rational expressions: If the denominators of two rational expressions are already the same, then we can add/subtract their numerators directly. To add/subtract rational expressions, first rewrite the fractions with a common denominator. Thus, the simplest form is (y + 2) / (2y + 3), where y ≠ 0, -3/2.Īdding and Subtracting Rational Expressions Note that we shouldn't use the denominator of the simplest form while calculating the restrictions. To find the restrictions, set the original denominator ≠ 0 and solve. To simplify the given expression, we just factorize the numerator and denominator and cancel the common terms. Note that the restrictions are any values that make the denominator equal to 0, including any canceled terms while simplifying.Įxample: Simplify the rational expression (3y 2 + 6y) / (6y 2 + 9y). Step 4: Mention the restricted values if any.Step 3: Write the remaining terms in the numerator and denominator.Step 1: Factorize each of the numerator and the denominator by taking the common factors out.Let us look at the steps to be followed for simplifying rational expressions. The same thing works for simplifying rational expressions as well but the only difference is of having polynomials in the fraction. In fractions, when the numerator and denominator of a rational number have no common factor other than 1, we consider that it is its simplified form. The simplification of a rational expression is the same as how we simplify fractions.

$multiplying and dividing rational expressions$

Simplifying rational expressions means reducing the value of a rational expression to its lowest terms or simplified form. Thus, to find the restriction(s) of a rational expression just set the denominator equal to 0 and solve for the variable. In other words, we say x / (x + 2) takes all values for x but x ≠ -2.

For example, in the expression x / (x + 2), the denominator becomes zero when x = -2 and hence it is known as the restriction of the rational expression x / (x + 2). Thus, a rational expression (as it is a fraction) is NOT defined for the value(s) of the variable for which the denominator is equal to 0. Check what is 1/0 using your calculator, it will throw an error. Note that if one of the numerator and denominator is NOT a polynomial, then the fraction is NOT called as a rational expression.ĭividing a number by 0 is not possible. Here are some examples of rational expressions: (x + 1) / (x 2 - 5), (x 3 + 3x 2 - 5) / (4x - 2), etc. Since rational expressions are nothing but fractions, we operate on them just the way we operate the fractions. i.e., it is of the form p(x)/q(x), where q(x) ≠ 0 and p(x) and q(x) are polynomials. In a rational expression, both numerator and denominator are polynomials. Together you can come up with a plan to get you the help you need.Rational expressions are fractions with variables. See your instructor as soon as possible to discuss your situation. You need to get help immediately or you will quickly be overwhelmed. …no - I don’t get it! This is critical and you must not ignore it. Is there a place on campus where math tutors are available? Can your study skills be improved?

Who can you ask for help? Your fellow classmates and instructor are good resources. It is important to make sure you have a strong foundation before you move on. Math is sequential - every topic builds upon previous work. This must be addressed quickly as topics you do not master become potholes in your road to success. What did you do to become confident of your ability to do these things? Be specific! Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. I can.ĭetermine the values for which a rational expression is undefined. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. Simplify by dividing out common factors.Ī.Multiply the numerators and denominators together.Factor the numerators and denominators completely.Rewrite the division as the product of the first rational expression and the reciprocal of the second.

Multiplying and dividing rational expressions