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

1 Answer
Mar 29, 2017

Answer:

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

Explanation:

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:
enter image source here