Question 700408
When you add fractions you must use a common denominator.  For example 1/2 + 1/2 = 2/2, but you can't add 1/3 + 1/2 - it's like adding 1 apple to 1 orange.<P>
You must find a common denominator.  In 1/2 + 1/3 the common denominator is 6.  6/2=3 so multiply the numerator of 1/2 by 3 (1*3=3) to convert that fraction to 3/6.  For 1/3 6/3=2 and 2*1=2 so that converts to 2/6.<P>
Now you can add the fractions 3/6 + 2/6 = 5/6.<P>
The same is true in this problem. {{{1- 5/x -6/x^2}}} is adding/subtracting fractions.  You must have a common denominator.  In this case the common denominator is {{{x^2}}}.<P>
1 is the same as 1/1.  {{{x^2 / 1 = x^2}}} so multiply the numerator by {{{x^2}}}.  The converted fraction is {{{x^2 / x^2}}}.<P>
Convert -5/x --->{{{x^2 / x = x}}} and x*-5 is -5x.  The converted fraction is {{{-5x/x^2}}}.<P>
{{{6/x^2}}} already has the common denominator so it needs no conversion.<P>
The problem has now become {{{x^2 / x^2 - 5x/x^2 + 6/x^2}}}.  Since they share the same denominator you can rewrite as the sum/difference of the numerators all over the denominator:<P>
{{{(x^2-5x+6)/x^2}}}
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