It is perfectly OK to use .  You will get the same answer
if you do it correctly.  You just made a mistake.

The reason they tell you to use  is because they
want ONE rule to work for all problems.

When you have 



They always tell you to multiply by the conjugate of the denominator
over itself:



You problem  is really the same as ,
so to follow that rule you would multiply by ,
which is the same as .

It would also work to use  but they don't
want to tell you to multiply by the negative of the conjugate of
the denominator over itself.

Using 







Since ,



Separate into two fractions: 







----------------------------------

Or you can use 







Since ,










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Edwin