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What are the excluded values for #y=(x+1)/(x-3)#?

Answer 1

Eli Assouline

Excluded values: #x=3# and #y=1#

Given
#color(white)("XXX")y=(x+1)/(x-3)#
since division by zero is undefined, we must exclude
#color(white)("XXX")x=3#

Re-writing the given equation:
#color(white)("XXX")yx-3y=x+1#

#color(white)("XXX")yx-x=3y+1#

#color(white)("XXX")x(y-1)=3y+1#

#color(white)("XXX")x=(3y+1)/(y-1)#

and (again) since division by zero is undefined, we must exclude:
#color(white)("XXX")y=1#

This can also be seen graphically by plotting the given equation:

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Answer 2

Genesis Allen

The excluded value for y=(x+1)/(x-3) is x=3.

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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.