SOLUTION: what are rational expressions? Why must we always be mindful of the final value of the denominator in a rational expression? For example, consider the rational expression 3x/(x2 �

Question 369235: what are rational expressions? Why must we always be mindful of the final value of the denominator in a rational expression? For example, consider the rational expression 3x/(x2 � 16). What values in the denominator must we be mindful of? Explain why.

Answer by lefty4ever26(59) (Show Source): You can put this solution on YOUR website!
A rational expression is the ratio of 2 polynomials...
ex:

We must be mindful of the final value of the denominator because the expression would be undefined whenever the denominator equals 0.
In your example: Set the denominator equal to 0 and solve for x.
Factor
Set each factor equal to 0.
x-4=0 x+4=0
x=4, x=-4 SO the expression is undefined at x=4 and x=-4. This is important when you graph the equation because there would be vertical asymptotes at x=4 and x=-4 where the graph would either extend up towards infinity or down towards negative infinity. The graph of this equation is below

You can see how the graph never reaches x=-4 or x=4. It just extends of the graph at those x values.
Hope this helps you understand a bit about rational expressions.

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