What real values of x are not in the domain of $f(x) = \frac{1}{|x^2 + 3x - 4| + |x^2 + 9x - 10|}$?
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x2 + 3x – 4 = (x – 1)(x + 4)
x2 + 9x – 10 = (x – 1)(x + 10)
When x=1, both (x2 + 3x – 4) and (x2 + 9x – 10) equal zero
So, when x=1, (x2 + 3x – 4) + (x2 + 9x – 10) = 0 + 0 which
puts a zero in the denominator, and you can't divide by zero.
Therefore, when x = 1 the fraction is 1/0 which is undefined.
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