Question 1126069
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Simplify:  {{{((3^(2n)) - 1) / ((3^(n+1)) - 3)}}}<br>
The numerator factors as the difference of squares:<br>
{{{3^(2n)-1 = (3^n-1)(3^n+1)}}}<br>
In the denominator, take one factor of 3 out of "3^(n+1)"; then factor out the common factor of the two terms:<br>
{{{3^(n+1)-3 = 3(3^n)-3 = 3(3^n-1)}}}<br>
Now simplify:<br>
{{{((3^(2n)) - 1) / ((3^(n+1)) - 3) = ((3^n-1)(3^n+1))/((3)(3^n-1)) = (3^n+1)/3}}}