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T(x)=(x+5)/(x²-2x-24) The domain in interval notation is

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Final answer:

The domain of the function t(x)=(x+5)/(x²-2x-24) is (-∞, -4) ∪ (-4, 6) ∪ (6, ∞) in interval notation.

Step-by-step explanation:

The domain of a function is the set of all possible input values, or x-values, for which the function is defined. In this case, the function t(x)=(x+5)/(x²-2x-24) is defined for all values of x except the ones that would make the denominator equal to zero.

To find the domain, we need to solve the equation x²-2x-24=0. This equation can be factored to (x-6)(x+4)=0, which means that x=6 or x=-4.

Therefore, the domain of the function is (-∞, -4) ∪ (-4, 6) ∪ (6, ∞) in interval notation.

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