Question 38591
{{{(4x)/(x^2-18x+72) + 4/(x-6) }}}


Notice that the first denominator probably factors, and looking at the second denominator you might suspect that one of the factors is (x-6).  Indeed it is!! The first denominator factors into (x-6)(x-12).  Isn't that a coincidence???


{{{(4x)/((x-6)*(x-12)) + 4/(x-6) }}}


In order to get a common denominator, you need to multiply the numerator and denominator of the second fraction by (x-12).  It should now look like this:

{{{(4x)/((x-6)*(x-12)) + (4/(x-6))*((x-12)/(x-12)) }}}


Now, the denominator of the answer is the LCD, which is (x-6)(x-12).
To get the numerator, just add the numerators of the two fractions:

{{{(4x)/((x-6)*(x-12)) + (4/(x-6))*((x-12)/(x-12)) }}}
{{{(4x + 4*(x-12) )/((x-6)*(x-12)) }}}
{{{(4x + 4x - 48) / ((x-6)*(x-12) ) }}}
{{{(8x-48)/((x-6)*(x-12)) }}}


This factors into 
{{{(8*(x-6))/((x-6)*(x-12)) }}}


and the fraction reduces by dividing out the (x-6) factors:
{{{8/(x-12)}}}


Nice problem!!  I'm sorry no one answered it earlier for you!  I have not had much time lately!


R^2 at SCC