Question 146886
Find Sum. 
{{{4/(3a-6)+a/(2+a)}}}
<pre><font size = 4 color = "indigo"><b>
You can use this principle for adding two fractions:

{{{(UPPER_LEFT)/(LOWER_LEFT)+(UPPER_RIGHT)/(LOWER_RIGHT)}}} =

{{{((UPPER_LEFT)(LOWER_RIGHT)+(UPPER_RIGHT)(LOWER_LEFT))/((LOWER_LEFT)*(LOWER_RIGHT))}}} 

{{{(4(2+a)+a(3a-6))/(3a-6)(2+a)}}}

Multiply out the top and bottoms:

{{{(8+4a+3a^2-6a)/(6a+3a^2-12-6a)}}}

Combine like terms:

{{{(8-2a+3a^2)/(3a^2-12)}}}

Write the top in descending order:

{{{(3a^2-2a+8)/(3a^2-12)}}}

You can factor the bottom as {{{3(a-2)(a+2)}}}
if you like, but there is no reason to, because
the top doesn't factor.  But if you like you
can express the final answer as:

{{{(3a^2-2a+8)/(3(a-2)(a+2))}}}

Edwin</pre>