We have to be careful here! We might be tempted
to use the zero-factor principle. However that
will lead us astray because is not
defined at ANY of the values of x for which
!
So do NOT do this:
Instead use the identity to replace .
We can cancel 's as long as we are careful
not to allow any values of x which cause the
denominator to be zero.
That leaves:
which has solution
, where n is any integer.
And this is a valid solution since
is always either or , and never .
Edwin
