Question 36284
{{{y/ (y^2-49)  + 7 /(y^2+8y+7) }}}


The first step is to factor the denominators so you can find the LCD:
{{{y/ ((y-7)*(y+7))  + 7 /((y+7)*(y+1)) }}}


Next, you must compare each denominator to the LCD, and decide what factors are missing from each of the denominators.   Notice the in the first denominator, you are missing a factor of (y+1), and in the second denominator, you are  missing a factor of (y-7).  So multiply the first fraction by {{{(y+1)/(y+1) }}} and multiply the second fraction by the missing factor which is {{{ (y-7)/(y-7) }}}.  It should look like this:

{{{(y/ ((y-7)*(y+7)))*((y+1)/(y+1))  + (7 /((y+7)*(y+1)))*((y-7)/(y-7)) }}}



Now that you have a common denominator for the fractions, you can multiply out the numerators and  place the result over the common denominator.


{{{ (y^2 +y+7y-49)/((y-7)*(y+7)*(y+1))}}}


Combine like terms in the numerator, and see if the numerator can be factored. In this case, it cannot, so what you have is the final answer:
{{{ (y^2 +8y-49)/((y-7)*(y+7)*(y+1))}}}


R^2 at SCC