3.

 

We are adding fractions, so we need common denominators. We don't have common denominators, so we have to find a common denominator. First factor both denominators.

 

 

At this point we see that both denominators already have a factor of 2x + 5 in common. The first one does not have the x + 3 which the second one has, and the second denominator does not have the x - 4 which the first one has. So we multiply top and bottom of the first fraction by x + 3 and top and bottom of the second one by x - 4.

 

 

Now that we have common denominators, we can add the tops. First remove parentheses.

 

 

Then combine like terms on the top.

 

 

Now that we have finished the addition process, we still should check to see if this fraction will reduce. Fortunately, we cleverly left the bottom factored. Now that we have simplified the top, we can check to see if it will factor. It does.

 

 

Not only does the top factor, but one of the factors cancels with one of the factors on the bottom leaving us with a simplified answer of

 

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