I doubt that was what you were told- it's not true. You probably were told that the numerator must be at least one degree lower than the denominator. That's because if the degree of the numerator were greater than or equal to the degree of the denominator you could do a "long division" giving a polynomial plus a fraction in which the numerator does have degree less than the denominator.I was also told that the polynomial in the numerator should be 1 degree lower than the one in the denominator - why?
I'm not sure what you want. is defined (for real numbers) as the positive real number, y, such that . Because -y (and no other number) will also have that property, , from , it follows that or .Also, I was wondering.
why does that become
Again, I'm looking for a proof explanation so that I can remember it and derive it if I forget.