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 –

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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 –       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
A rational expression is the ratio of 2 polynomials...
ex:
%282x%5E2%2B3%29%2F%28x%5E3%2B3x-12%29
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: 3x%2F%28x%5E2-16%29 Set the denominator equal to 0 and solve for x.
x%5E2-16=0 Factor
%28x-4%29%28x%2B4%29=0 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
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C3x%2F%28x%5E2-16%29%29
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.