The least common denominator of the rational expression [x²/(x² - 16)] + [(9+x)/(8 · x + 2 · x²)] found by factor their denominators is 2 · (x + 4) · (x - 4).
Rational numbers are formed by numbers of the form n/m, where n and m are integers known as numerator and denominator, respectively. The least common denominator is the least denominator between a group of rational functions such that they get the same denominator.
In this case we have two denominators: x² - 16, 8 · x + 2 · x². We can determine the least common denominator by factoring each expression and discovering known terms:
x² - 16 = (x + 4) · (x - 4)
8 · x + 2 · x² = 2 · x · (x + 4)
The least common denominator of the rational expression [x²/(x² - 16)] + [(9+x)/(8 · x + 2 · x²)] found by factor their denominators is 2 · (x + 4) · (x - 4).
To learn more on least common denominators: https://brainly.com/question/8393834
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