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Find the domain for each expression.
1. (x^2 + 5x - 10)/(x^3 - x)
2. (-9x^2 - x + 1)/(x^3 + x)
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Question 1
(x^2 + 5x - 10)/(x^3 - x)
Set denominator to 0.
x^3 - x = 0
x(x^2 - 1) = 0
x = 0
x^2 - 1 = 0
x^2 = 1
sqrt{x^2} = sqrt{1}
x = -1, x = 1
Domain = {x | x cannot be 0, -1, or 1}
Question 2
(-9x^2 - x + 1)/(x^3 + x)
Set denominator to 0.
x^3 + x = 0
x(x^2 + 1) = 0
x = 0
x^2 + 1 = 0
When I subtract -1 from both sides of the equation, it leads to a situation involving complex numbers. The current chapter and section in the textbook does not ask for complex roots. So, I will say that x^2 + 1 is rejected.
Domain = {x | x cannot be 0}
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