If #p=4xy/(x+y)# then how much is #(p+2x)/(p−2x)+(p+2y)/(p−2y)#?
There may be a simpler way to get this result, but I am not certain that I have interpreted the question correctly, so I will just use a sledgehammer approach.
Note 1: I've used
but these are equivalent.
Note 2: I've also assumed that
Part 1: Simplifying
Part 2: Simplifying
Omitting the details but following the same process as above:
Part 3: Evaluating the Sum
The assumption that
but the effect of the other assumptions:
should be evaluated.
Let us use here the concept of Componendo and Dividendo. This essentially states that if
Their ratio gives us
Coming to the problem
Now applying Componendo and Dividendo, we get
applying Componendo and Dividendo, we get
Adding (A) and (B) , we get