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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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Matthew D. | Math and ChemistryMath and Chemistry
4.8 4.8 (8 lesson ratings) (8)
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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:
 
     [u(2x-u)]/[(x-u)(x+u)]