How do you simplify and list the restrictions for #h (x)= (t^2  3t  4 )/ (t^2 + 9t + 8)#?
with exclusion
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To simplify and list the restrictions for the function h(x) = (t^2  3t  4) / (t^2 + 9t + 8), we can factor the numerator and denominator and cancel out any common factors.
The numerator can be factored as (t  4)(t + 1), and the denominator can be factored as (t + 1)(t + 8).
Canceling out the common factor (t + 1), we get h(x) = (t  4) / (t + 8).
The restriction for this function is that t cannot be equal to 1 or 8, as these values would result in division by zero.
Therefore, the simplified function h(x) = (t  4) / (t + 8) is valid for all real numbers except t = 1 and t = 8.
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To simplify the rational function h(x) = (t^2  3t  4) / (t^2 + 9t + 8) and list the restrictions:

Factor the numerator and denominator: Numerator: t^2  3t  4 factors to (t  4)(t + 1) Denominator: t^2 + 9t + 8 factors to (t + 8)(t + 1)

Rewrite the function with factored terms: h(t) = ((t  4)(t + 1)) / ((t + 8)(t + 1))

Cancel out common factors in the numerator and denominator: h(t) = (t  4) / (t + 8)

List the restrictions: The function h(x) is undefined when the denominator is equal to zero. So, t + 8 cannot be zero, which means t ≠ 8. Additionally, since there are no factors in the simplified expression that would result in the numerator being zero, there are no additional restrictions. Therefore, the only restriction is that t ≠ 8.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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