# If #p=4xy/(x+y)# then how much is #(p+2x)/(p−2x)+(p+2y)/(p−2y)#?

##### 2 Answers

If

then

#### Explanation:

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 #(p+2x)/(p-2x)#**

**Part 2: Simplifying #(p+2y)/(p-2y)#**

Omitting the details but following the same process as above:

**Part 3: Evaluating the Sum #(p+2x)/(p-2x)+(p+2y)/(p-2y)#**

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The assumption that

but the effect of the other assumptions:

should be evaluated.

#### Explanation:

Let us use here the concept of **Componendo and Dividendo**. This essentially states that if

As **Componendo**.

and subtracting **Dividendo**.

Their ratio gives us **Componendo and Dividendo** together.

Coming to the problem

i.e.

Now applying **Componendo and Dividendo**, we get

**...............(A)**

and as

applying **Componendo and Dividendo**, we get

**...............(B)**

Adding **(A)** and **(B)** , we get

#=(3y+x)/(y-x)+(3x+y)/(x-y)#

#=(-3y-x+3x+y)/(x-y)#

#=(2x-2y)/(x-y)=2#