How do you simplify and list the restrictions for #h (x)= (t^2 - 3t - 4 )/ (t^2 + 9t + 8)#?

Answer 1

#h(t) = (t^2-3t-4)/(t^2+9t+8) =1 - 12/(t+8)#

with exclusion #t != -1#

#h(t) = (t^2-3t-4)/(t^2+9t+8)#
#=(t^2+9y+8-12t-12)/(t^2+9t+8)#
#=(t^2+9y+8)/(t^2+9t+8)-(12(t+1))/(t^2+9t+8)#
#=1 - (12(t+1))/((t+1)(t+8)#
#=1 - 12/(t+8)#
with exclusion #t != -1#
The value #t = -1# is excluded because it results in both the numerator and denominator of #h(x)# becoming #0# and #0/0# is indeterminate.
Note that #t = -8# is not an excluded value from this simplification, since it is equally a singularity of #h(x)# and #1-12/(t+8)#.
The domain of both is #(-oo, -8) uu (-8, oo)#
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Answer 2

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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Answer 3

To simplify the rational function h(x) = (t^2 - 3t - 4) / (t^2 + 9t + 8) and list the restrictions:

  1. 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)

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

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

  4. 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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Answer from HIX Tutor

When evaluating a one-sided 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 one-sided 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 one-sided 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 one-sided 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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