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Find the domain of the function $$\frac{x^4-4x^3+6x^2-4x+1}{x^2-4}$$.

Oct 15, 2019

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The only values of x where the domain is not defined is where x^2  - 4  = 0

So

x^2 - 4  = 0

(x + 2)(x - 2)  = 0

Setting each factor to 0  and solving for x  gives us that   x =  -2  and x  = 2

Look at the graph here :  https://www.desmos.com/calculator/ph4j7rnvab

The domain exists on (-infinity, -2)  U  (-2, 2)  U  (2, infinity)

Oct 15, 2019