Question 79994
<pre><font size = 5><b>
Divide the polynomial 

{{{(3x^n+6x^(n-1)-2x^(n-2))/2x^(n-1)}}}

Make three fractions, placing each term over the same 
denominator:

{{{3x^n/2x^(n-1) + 6x^(n-1)/2x^(n-1) - 2x^(n-2)/2x^(n-1)     }}}

In the second fraction cancel the 2 into the 6
In the third fraction cancel the 2's

{{{3x^n/2x^(n-1) + 3x^(n-1)/x^(n-1) - x^(n-2)/x^(n-1)     }}} 

Subtract exponents of x

{{{ 3x^(n-(n-1)) /2 + 3x^((n-1)-(n-1)) - x^((n-2)-(n-1)) }}}

Remove the parentheses in the exponents

{{{ 3x^(n-n+1) /2 + 3x^(n-1-n+1) - x^(n-2-n+1) }}}

Simplify the exponents:

{{{ 3x^1/2 + 3x^0 - x^-1 }}}

Erase the 1 exponent in the first term
Replace {{{x^0}}} by 1
Replace {{{x^-1}}} by {{{1/x}}}

{{{(3x)/2 + 3(1) - 1/x }}}

Replace {{{3(1)}}} by just 3:

{{{(3x)/2 + 3 - 1/x }}}

Edwin</pre>