Question 706951
In the future, please put parentheses around multiple-term numerators and denominators. Without the parentheses it is difficult for us to determine what is in a numerator or denominator and what is in separate terms. What you posted meant:
{{{n^2+3n+2/n^2+6b+8 - 2n/n+4}}}
which is probably not what you meant. Clearly expressed problems are more like to get quick responses.<br>
I'm guessing you meant:
{{{(n^2+3n+2)/(n^2+6b+8) - 2n/(n+4)}}}
If this is correct then keep reading. If not then re-post your question using parentheses to make it clear.<br>
First let's factor the numerators and denominators. This will help us:<ul><li>find the lowest common denominator; and</li><li>possibly reduce some fractions</li></ul>The numerator and denominator in the first fraction will each factor:
{{{((n+2)(n+1))/((n+2)(x+4)) - 2n/(n+4)}}}
As we can see, there is a factor we can cancel in the first fraction:
{{{(cross((n+2))(n+1))/(cross((n+2))(x+4)) - 2n/(n+4)}}}
leaving:
{{{(n+1)/(x+4) - 2n/(n+4)}}}
Not only did the first fraction reduce but we got common denominators at the same time! So we can proceed with the subtraction:
{{{((n+1) - (2n))/(n+4)}}}
which simplifies to:
{{{(-n+1)/(n+4)}}}