What are the excluded values for #(5x+1)/(x^2-1)#?

Answer 1

See the entire solution process below:

Because we cannot divide by #0# the excluded values are:
#x^2 - 1 != 0#
We can factor #x^2 - 1# using the rule:
#a^2 - b^2 = (a + b)(a - b)#
Letting #a^2 = x^2#, #a =x#, #b^2 = 1# and #b = 1# and substituting gives:
#(x + 1)(x - 1) != 0#
Now, solve each term for #0# to find the excluded values of #x#:

Solution 1)

#x + 1 = 0#
#x + 1 - color(red)(1) = 0 - color(red)(1)#
#x + 0 = -1#
#x = -1#

Solution 2)

#x - 1 = 0#
#x - 1 + color(red)(1) = 0 + color(red)(1)#
#x - 0 = 1#
#x = 1#
The excluded values are: #x = -1# and #x = 1#
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Answer 2

The excluded values for (5x+1)/(x^2-1) are x = -1 and x = 1.

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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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