why does 9/x^2 -1 simplify to 9-x^2/x^2 . is it because we need to reduce the expression to one term?

Question

datanewb · Answer

$$\frac{9}{x^2} - 1 = \frac{9-x^2}{x^2} $$

Notice that 1 can be rewritten as $$\frac{x^2}{x^2}$$ You can try any value of for x, and it will always reduce to 1/1 = 1.

So then we have: $$\frac{9}{x^2} - \frac{x^2}{x^2} $$ and since those have common denominators, we can just subtract the numerators to get $$\frac{9-x^2}{x^2} $$

anonymous · Answer

So are we ending up with an expression that is supposed to be simpler than the original, and why?

datanewb · Answer

Oh, sorry, I see what you are asking.  I think it depends on the situation as to which side is simpler. 

I guess the right side might be simpler for computation, because you can simply input values for x when calculating it's value without then having to do the extra step of finding a common denominator, but for the most part I find both sides equally simple/complex.

anonymous · Answer

Ok, thanks, I thought it was cast in stone that it had to be simplified.  Your answer really helps!