Adding Rational Expressions

Do you know what rational expressions mean? How do you explain it to your kids so they understand this advanced concept of math? Adding rational expressions together is the fundamental skill necessary to move up to more difficult algebraic problems in the future.

A rational expression is simply a fraction in which the numerator and denominator are polynomials. To solve for an addition equation for rational expressions, you will first have to consider whether the denominator is the same and reduced to its lowest terms. For example, if you are given the following problem:

You will first observe that the denominators are the same, which in this case is 5xy. Next, add the expressions together but note that the denominator does not change. You will get the following:

Then, you will need to simplify the fraction to its lowest terms. This means that you have to “cancel out” the common variables between the numerator and denominator. Since the common variable for the fraction is x, after simplifying the fractions, you will get this:

Since fractions work like division, once you get 10/5y, you can reduce the fraction even further by dividing the 10 and 5, which gives you 2.

For rational expressions with different denominators, you must first factor each denominator separately and completely, then reduce it to its lowest terms, and simplify like you normally would with regular fractions.

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