Question 450798
find the domain of x+4/x^2+x-6
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When we are trying to find the domain of a function, we are looking for x-values that would make the function invalid or undefined.  We know that if the denominator is = 0, the function is undefined. So, we set the denominator=0, and solve for the x-value(s) that make the denominator=0. When we find these x-values, we say they are not in the domain.
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setting denominator=0
x^2+x-6=0
solve by factoring
(x+3)(x-2)=0
x=-3
or
x=2
We can now say, -3 and 2 are not in the domain.
or All real numbers except -3 and 2
or in interval notation: (-∞,-3) U (-3, 2) U (2, ∞)