Simplifying Rational Expressions

Rational, do you know what that term means?  When you hear the word “rational” I like you to think of the word “fraction”.  The difference between rational and fractions is rational expressions have variable terms (polynomials) in there numerators and denominators and fractions just have numbers. So, simplifying rational expressions is very much like simplifying “fraction” expressions which you know as reducing/simplifying a fraction.  Example, lets say I tell you to simplify the fraction 10 / 50 .  As a super smart student you would notice that 10 is a common factor of the numerator and denominator leading you to the simplified fraction 1 / 5.   When we use the term “simplifying” we basically mean “reduce” just like our example.  OK now I’m ready to make my point-  simplifying rational expressions is when we “reduce” fractions with variables.  The key skill to simplify these expressions is factoring- you have to be able to find like/common factors among the numerator and denominator.   These like factors are your target to cancel out as I show in the examples below.  So, if you understand what I just said and can factor you should be fine!  This is a very important algebra skill so take it seriously….good luck!




some key topics that involve rational expression skills:

* rational equations
* ratios and proportions
* fractions
* graphing rational functions


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