How do you simplify and state the excluded values for #(y+5) /( y^2+4y-32)#?

Answer 1
#(y+5)/(y^2+4y-32) = (y+5)/((y+8)(y-4))#
If you like, you can eliminate #y# from the numerator, by writing:
#(y+5)/((y+8)(y-4)) =((y-4) + 9)/((y+8)(y-4))#
#=1/(y+8)+9/((y+8)(y-4))#

or in writing:

#(y+5)/((y+8)(y-4)) =((y+8) - 3)/((y+8)(y-4))#
#=1/(y-4) - 3/((y+8)(y-4))#
In any case, the excluded values are #y=4# and #y=-8#
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Answer 2

To simplify the expression (y+5) /( y^2+4y-32), we can factor the denominator. The factored form of the denominator is (y+8)(y-4). Therefore, the simplified expression is (y+5) / (y+8)(y-4).

To find the excluded values, we need to identify the values of y that would make the denominator equal to zero. In this case, the excluded values are y = -8 and y = 4, as they would result in division by zero.

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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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