Add and Simplify

Question

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

Answer 1

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)]