SOLUTION: (9-x^-2)/(3+x^-1) ? a) 3x-1/x^2 b) 3x+1/x^2 c) 3x+1/x d) x(3x-1) e) 3x-1/x

Question 1044832: (9-x^-2)/(3+x^-1) ?
a) 3x-1/x^2
b) 3x+1/x^2
c) 3x+1/x
d) x(3x-1)
e) 3x-1/x
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It is E. Here is why.
Write the numerator as 9-(1/x^2). Common denominator of x^2 and get (9x^2-1)/x^2 and write it as
(3x+1)(3x-1)/x^2, a difference of squares. This is the numerator.
The denominator is 3+(1/x). That is (3x+1)/x
We cancel a (3x+1) in both and an x in both.
That leaves (3x-1)/x, or E.
Sometimes you want negative exponents, other times you want to write them as fractions. Here, the latter works better.
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