Question

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

Answer 1

`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`