Course: Intermediate Algebra
Topic: Rational Expressions
Subtopic: Operations I - Evaluate & Simplify


Our goal today is to work with algebraic fractions (a.k.a. rational expressions). All the operations you learned to do with numeric fractions in grade school (multiply, "flip and multiply" to divide, LCDs to add, etc.) we will be learning except that the numerator and denominator of our fractions will be polynomials. 

Be sure that you recognize opposites (like x-1 and 1-x) and how to handle them when cancelling or finding LCDs.

Don't worry too much about the graphical representation of "excluded values" a.k.a. "domain restrictions", but you should recognize algebraically that there are x-values that can't be plugged into a rational expression because they cause the denominator to be zero (e.g., in the expression 2/(x+5) x cannot be -5) which is undefined. You can find the domain restrictions by factoring the denominator of the rational expression and determining what x-values would make it zero, i.e. set it equal to zero and solve for x.

Caution: when reducing a rational expression like (2x2-50)/(x+5) do not cancel the x's nor reduce the 5's! This is a very common error, tempting, but extremely illegal. Remember that you can only cancel factors not terms. So before canceling you must factor completely! Never reduce a rational expression without factoring top and bottom completely first.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: rational, rational function, domain, domain restrictions (a.k.a. excluded values), vertical asymptote line

Text Notes