# Calculus

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Find the domain:

f(x)= x2-7x+12/x4-8x3+13x2+30x-72

• Calculus -

Do not forget the parentheses:
f(x)= (x2-7x+12)/(x4-8x3+13x2+30x-72)

The domain of f(x) is the intersections of the domain of the numerator and denominator, less the zeroes of the denominator.

The domain of polynomials is ℝ, for both the numerator and denominator. The roots of the denominator can be found by factorization, = (x-4)(x-3)²(x+2)
So at these values of x, there will be a vertical asymptote, and these three values have to be deducted from the domain.

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