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Add and Simplify

Add  XU/X2-U2+U/X+U Simplify your answer. Type your answer in factored form.
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1 Answer

I am assuming the question is in the following form:
xu/(x2-u2) + u/(x+u)
1. Cross multiply to get a common denominator and add the two together.      
[xu(x+u) + u(x2-u2)] / [(x2-u2)(x+u)]
2. Notice the bold section in the numerator above. We can factor out              
(x2-u2) to -> (x+u)(x-u)
2a. Our equation now looks like
[xu(x+u) + u((x-u)(x+u))] / [(x2-u2)(x+u)]
3. Cancel out (x+u) from the numerator and denominator.
[xu(x+u) + u((x-u)(x+u))] / [(x2-u2)(x+u)]
4. Simplify your numerator and factor the denominator which gives our final answer of: