Topic : Polynomials-Difference of squares
from: category_eng
1. '

The fraction frac{left(3^{2008} ight)^2-left(3^{2006} ight)^2}{left(3^{2007} ight)^2-left(3^{2005} ight)^2} simplifies to which of the following?

mathrm{(A)} 1qquadmathrm{(B)} frac{9}{4}qquadmathrm{(C)} 3qquadmathrm{(D)} frac{9}{2}qquadmathrm{(E)} 9

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1.

Notice that 9 can be factored out of the numerator:
frac{left(3^{2008}<br /> ight)^2-left(3^{2006}<br /> ight)^2}{left(3^{2007}<br /> ight)^2-left(3^{2005}<br /> ight)^2}=frac{9left(3^{2007}...
Thus, the expression is equal to 9, and the answer is mathrm{(E)}.