Is #2=(x+1)/(x-1)# a conditional equation? If it is, what is one value of x that makes it false?

1 Answer
Sep 3, 2017

#2=(x+1)/(x-1)# is false for any #x!=3#

For example, this equation is false if #x=100#

Explanation:

We could start with the obvious problem of #x=1#
If #x=1# then #(x+1)/(x-1)# is undefined and #2# can not be equal to an undefined value.

If #x!=1#
then we can rearrange the equation to be
#color(white)("XXX")2(x-1)=x+1#

#color(white)("XXX")rarr 2x-2=x+1#

#color(white)("XXX")rarr x=3#
That is the only value for which this equation can be true is #x=3#.

This could be written as a conditional equation:
#color(white)("XXX")2=(x+1)/(x-1)color(white)("xxx")"if and only if "x=3#